Patent Publication Number: US-2022231642-A1

Title: Amplifier with switchable transformer

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority to and the benefit of Provisional Patent Application No. 63/139,259, filed in the United States Patent and Trademark Office on Jan. 19, 2021, the entire specification of which is incorporate herein as if fully set forth below in its entirety and for all applicable purposes. 
    
    
     BACKGROUND 
     Field 
     Aspects of the present disclosure relate generally to wireless communications, and, more particularly, to an amplifier with a switchable transformer. 
     Background 
     A wireless device includes a transmitter for transmitting signals via one or more antennas. The transmitter may include multiple amplifiers to amplify signals before the signals are transmitted. The amplifiers may include variable gain amplifiers (VGAs), driver amplifiers, and power amplifiers (PAs). A transformer may be used as a load of an amplifier to implement a bandpass filter for amplifying signals within a desired frequency band. A transformer may also be used in the transmitter to convert a differential signal into a single-ended signal, convert a single-ended signal into a differential signal, and/or provide impedance matching. 
     SUMMARY 
     The following presents a simplified summary of one or more implementations in order to provide a basic understanding of such implementations. This summary is not an extensive overview of all contemplated implementations and is intended to neither identify key or critical elements of all implementations nor delineate the scope of any or all implementations. Its sole purpose is to present some concepts of one or more implementations in a simplified form as a prelude to the more detailed description that is presented later. 
     A first aspect relates to an apparatus. The apparatus includes a first amplifier having a first output and a second output, and a transformer. The transformer includes a first switchable inductor coupled between the first output and the second output, a first capacitor coupled in parallel with the first switchable inductor, a second switchable inductor magnetically coupled to the first switchable inductor, a second capacitor coupled in parallel with the second switchable inductor, a third switchable inductor magnetically coupled to the first switchable inductor, and a third capacitor coupled in parallel with the third switchable inductor. 
     A second aspect relates to a method for operating an apparatus. The apparatus includes a first amplifier, and a transformer including a first switchable inductor coupled to the first amplifier, a second switchable inductor magnetically coupled to the first switchable inductor, and a third switchable inductor magnetically coupled to the first switchable inductor. The method includes, in a first mode, switching the first switchable inductor to a first inductance, enabling the second switchable inductor, and disabling the third switchable inductor. The method also includes, in a second mode, switching the first switchable inductor to a second inductance, disabling the second switchable inductor, and enabling the third switchable inductor. 
     A third aspect relates to an apparatus. The apparatus includes a first amplifier having a first output and a second output, and a transformer. The transformer includes at least one first inductor, at least one second inductor, wherein the at least one first inductor and the at least one second inductor are coupled between the first output and the second output of the first amplifier, and at least one first switch coupled in parallel with the at least one second inductor. The transformer also includes at least one third inductor magnetically coupled to the at least one first inductor and the at least one second inductor, at least one second switch coupled in series with the at least one third inductor, and a second capacitor coupled in parallel with the at least one second inductor and the at least one second switch. The transformer further includes at least one fourth inductor magnetically coupled to the at least one first inductor, at least one third switch coupled in series with the at least one fourth inductor, and a third capacitor coupled in parallel with the at least one fourth inductor and the at least one third switch. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an example of an amplifier with a transformer according to certain aspects of the present disclosure. 
         FIG. 2  shows an exemplary implementation of an amplifier according to certain aspects of the present disclosure. 
         FIG. 3  shows an example in which the transformer provides a wideband frequency response covering multiple frequency bands according to certain aspects of the present disclosure. 
         FIG. 4A  shows an example of an amplifier with a switchable transformer according to certain aspects of the present disclosure. 
         FIG. 4B  shows an example of amplifiers coupled to the switchable transformer via coupling capacitors according to certain aspects of the present disclosure. 
         FIG. 4C  shows another example of an amplifier with a switchable transformer according to certain aspects of the present disclosure. 
         FIG. 5A  shows an exemplary frequency response in a first mode according to certain aspects of the present disclosure. 
         FIG. 5B  shows an exemplary frequency response in a second mode according to certain aspects of the present disclosure. 
         FIG. 6  shows an exemplary implementation of a switching circuit according to certain aspects of the present disclosure. 
         FIG. 7A  shows an exemplary inductor according to certain aspects of the present disclosure. 
         FIG. 7B  shows an example of the inductor in  FIG. 7A  in which one portion of the inductor crosses another portion of the inductor according to certain aspects of the present disclosure. 
         FIG. 8A  shows another exemplary inductor according to certain aspects of the present disclosure. 
         FIG. 8B  shows an example of the inductor in  FIG. 8A  in which one portion of the inductor crosses another portion of the inductor according to certain aspects of the present disclosure. 
         FIG. 9  shows yet another exemplary inductor according to certain aspects of the present disclosure. 
         FIG. 10  shows an example in which the exemplary inductors shown in  FIGS. 7A, 8A and 9  overlap to form a switchable transformer according to certain aspects of the present disclosure. 
         FIG. 11  shows an example of a system including a switchable transformer and multiple amplifiers according to certain aspects of the present disclosure 
         FIG. 12  shows an example of a transmitter including a power amplifier and an antenna according to certain aspects of the present disclosure. 
         FIG. 13  shows an example of a transmitter including an antenna array according to certain aspects of the present disclosure. 
         FIG. 14  shows another example of a transmitter including a power amplifier and an antenna according to certain aspects of the present disclosure. 
         FIG. 15  shows another example of a transmitter including an antenna array according to certain aspects of the present disclosure. 
         FIG. 16  is a diagram of an environment including an electronic device that includes a transceiver according to certain aspects of the present disclosure. 
         FIG. 17  is a flowchart illustrating an exemplary method for operating an apparatus according to certain aspects of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The detailed description set forth below, in connection with the appended drawings, is intended as a description of various configurations and is not intended to represent the only configurations in which the concepts described herein may be practiced. The detailed description includes specific details for the purpose of providing a thorough understanding of the various concepts. However, it will be apparent to those skilled in the art that these concepts may be practiced without these specific details. In some instances, well-known structures and components are shown in block diagram form in order to avoid obscuring such concepts. 
       FIG. 1  shows an example of a system  110  in a transmitter according to certain aspects of the present disclosure. The system  110  is configured to amplify signals before the signals are transmitted via one or more antennas (not shown) coupled to the transmitter. In one example, the system  110  receives intermediate frequency (IF) signals from a previous stage (not shown) that converts baseband signals from a baseband processor into the IF signals. In this example, the system  110  amplifies the IF signals and outputs the amplified IF signals to a subsequent stage (not shown) that frequency upconverts the amplified IF signals into radio frequency (RF) signals for transmission. The IF signals may have frequencies in the gigahertz range. In other implementations, the system  110  may amplify RF signals. 
     In certain aspects, the system  110  is configured to amplify signals (e.g., IF signals) in multiple frequency bands. The multiple frequency bands may be used for different wireless communication technologies supported by the transmitter or may be used for the same wireless communication technology. In one example, the system  110  is configured to amplify signals in a first frequency band and signals in a second frequency band. The first frequency band and the second frequency band may be contiguous or non-contiguous. 
     In the example in  FIG. 1 , the system  110  includes a first amplifier  120 , a transformer  130 , a second amplifier  150 , and a third amplifier  160 . In one example, the first amplifier  120  is used to amplify signals in both the first frequency band and the second frequency band, the second amplifier  150  is used to amplify signals in the first frequency band, and the third amplifier  160  is used to amplify signals in the second frequency band. As discussed further below, the transformer  130  is used as a load for the first amplifier  120  to implement a bandpass filter having a wide passband covering both the first frequency band and the second frequency band. 
     In this example, the first amplifier  120  is a differential amplifier having a differential input and a differential output, in which the differential input includes a first input  122  and a second input  124 , and the differential output includes a first output  126  and a second output  128 . The outputs  126  and  128  of the first amplifier  120  are coupled to a primary side of the transformer  130  where the transformer  130  provides a load for the first amplifier  120 . In this example, the first amplifier  120  is configured to receive differential signals (e.g., differential IF signals) in both the first frequency band and the second frequency band from the previous stage (not shown) and drive the primary side of the transformer  130  based on the received differential signals. An exemplary implementation of the first amplifier  120  is discussed below with reference to  FIG. 2 . 
     The second amplifier  150  has a differential input including a first input  152  and a second input  154 . In the example shown in  FIG. 1 , the system  110  includes a first switch  172  coupled between the first input  152  of the second amplifier  150  and a secondary side of the transformer  130 , and a second switch  174  coupled between the second input  154  of the second amplifier  150  and the secondary side of the transformer  130 . As discussed further below, the second amplifier  150  is configured to amplify signals in the first frequency band in a first mode and output the amplified signals in the first frequency band to a subsequent stage (e.g., a first mixer for frequency upconversion to RF). 
     The third amplifier  160  has a differential input including a first input  162  and a second input  164 . The system  110  includes a third switch  176  coupled between the first input  162  of the third amplifier  160  and the secondary side of the transformer  130 , and a fourth switch  178  coupled between the second input  164  of the third amplifier  160  and the secondary side of the transformer  130 . As discussed further below, the third amplifier  160  is configured to amplify signals in the second frequency band in a second mode and output the amplified signals in the second frequency band to a subsequent stage (e.g., a second mixer for frequency upconversion to RF). Thus, in this example, signals in both frequency bands are amplified by the first amplifier  120 , signals in the first frequency band are further amplified by the second amplifier  150 , and signals in the second frequency band are further amplified by the third amplifier  160 . 
     In the first mode, a controller  180  turns on (i.e., closes) the first switch  172  and the second switch  174 , and turns off (i.e., opens) the third switch  176  and the fourth switch  178 . Thus, in the first mode, the differential input of the second amplifier  150  is coupled to the secondary side of the transformer  130  to amplify signals in the first frequency band. In the second mode, the controller  180  turns on (i.e., closes) the third switch  176  and the fourth switch  178 , and turns off (i.e., opens) the first switch  172  and the second switch  174 . Thus, in the second mode, the differential input of the third amplifier  160  is coupled to the secondary side of the transformer  130  to amplify signals in the second frequency band. Note that the individual connections between the controller  180  and the switches  172 ,  174 ,  176 , and  178  are not shown in  FIG. 1  for ease of illustration. 
     In the example in  FIG. 1 , the primary side of the transformer  130  includes a first inductor  144  and a first capacitor  142  coupled in parallel between a first terminal  132  and a second terminal  134  of the transformer  130 . The secondary side of the transformer  130  includes a second inductor  146  and a second capacitor  148  coupled in parallel between a third terminal  136  and a fourth terminal  138  of the transformer  130 . The first inductor  144  and the second inductor  146  are magnetically coupled (i.e., inductively coupled). The magnetic coupling transfers signal power from the primary side to the secondary side of the transformer  130 . 
     In this example, the differential output of the first amplifier  120  is coupled to the primary side of the transformer  130 . More particularly, the first output  126  of the first amplifier  120  is coupled to the first terminal  132  of the transformer  130  and the second output  128  of the first amplifier  120  is coupled to the second terminal  134  of the transformer  130 . 
     In this example, the first switch  172  is coupled between the first input  152  of the second amplifier  150  and the third terminal  136  of the transformer  130 , and the second switch  174  is coupled between the second input  154  of the second amplifier  150  and the fourth terminal  138  of the transformer  130 . 
     In this example, the third switch  176  is coupled between the first input  162  of the third amplifier  160  and the third terminal  136  of the transformer  130 , and the fourth switch  178  is coupled between the second input  164  of the third amplifier  160  and the fourth terminal  138  of the transformer  130 . 
     As discussed above, the first amplifier  120  drives the primary side of the transformer  130  based on differential signals (e.g., differential IF signals) received at the differential input of the first amplifier  120  from the previous stage (not shown). In this regard,  FIG. 2  shows an exemplary implementation of the first amplifier  120  according to certain aspects. In this example, the first amplifier  120  is a variable gain amplifier. 
     In the example in  FIG. 2 , the first amplifier  120  includes a first set of branches  230 - 1  to  230 - n  coupled between the first output  126  and ground, and a second set of branches  240 - 1  to  240 - n  coupled between the second output  128  and ground. Each branch in the first set of branches  230 - 1  to  230 - n  includes a respective input transistor  210 - 1  to  210 - n  and a respective switch  215 - 1  to  215 - n . In each branch in the first set of branches  230 - 1  to  230 - n , the gate of the respective input transistor  210 - 1  to  210 - n  (e.g., NFET) is coupled to the first input  122 , and the respective switch  215 - 1  to  215 - n  is coupled between the respective input transistor  210 - 1  to  210 - n  and the first output  126 . Each branch in the second set of branches  240 - 1  to  240 - n  includes a respective input transistor  220 - 1  to  220 - n  and a respective switch  225 - 1  to  225 - n . In each branch in the second set of branches  240 - 1  to  240 - n , the gate of the respective input transistor  220 - 1  to  220 - n  (e.g., NFET) is coupled to the second input  124 , and the respective switch  225 - 1  to  225 - n  is coupled between the respective input transistor  220 - 1  to  220 - n  and the second output  128 . 
     In this example, a gain controller (not shown) controls the gain of the first amplifier  120  by controlling the number of the branches  230 - 1  to  230 - n  and  240 - 1  to  240 - n  that are enabled using control signals C 1  to C n . The larger the number of branches that are enabled, the higher the gain. The gain controller enables a branch by closing the respective switch (e.g., respective one of the switches  215 - 1  to  215 - n  and  225 - 1  to  225 - n ) and disables a branch by opening the respective switch. In operation, the input transistor in each enabled branch in the first set of branches  230 - 1  to  230 - n  drives the first output  126  based on the voltage at the first input  122 . The input transistor in each enabled branch in the second set of branches  240 - 1  to  240 - n  drives the second output  128  based on the voltage at the second input  124 . Each of the switches  215 - 1  to  215 - n  and  225 - 1  to  225 - n  may be implemented with an NFET, a PFET, a transmission gate, or another type of switch. 
     It is to be appreciated that the first amplifier  120  is not limited to the exemplary implementation shown in  FIG. 2 . 
     Returning to  FIG. 1 , the transformer  130  implements a bandpass filter that causes the first amplifier  120  to amplify signals within a desired passband. The passband is a function of the primary resonance frequency of the transformer  130 , the secondary resonance frequency of the transformer  130 , and the coupling factor K between the first inductor  144  and the second inductor  146 . The coupling factor K is a measure of the magnetic coupling between the first inductor  144  and the second inductor  146 , as discussed further below. 
     The primary resonance frequency is given by the following: 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁢ 
                     
                       r 
                       1 
                     
                   
                   = 
                   
                     1 
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                         
                           
                             C 
                             1 
                           
                           ⁢ 
                           
                             L 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where fr 1  is the primary resonance frequency, C 1  is the capacitance of the first capacitor  142 , and L 1  is the inductance of the first inductor  144 . C 1  may also include parasitic capacitance at the outputs  126  and  128  of the first amplifier  120 . As shown in equation (1), the primary resonance frequency can be set to a desired frequency by choosing the capacitance of the first capacitor  142  and the inductance of the first inductor  144  accordingly. The secondary resonance frequency is given by the following: 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁢ 
                     
                       r 
                       2 
                     
                   
                   = 
                   
                     1 
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                         
                           
                             C 
                             2 
                           
                           ⁢ 
                           
                             L 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     where fr 2  is the secondary resonance frequency, C 2  is the capacitance of the second capacitor  148 , and L 2  is the inductance of the second inductor  146 . C 2  may also include parasitic capacitance at the inputs  152  and  154  of the second amplifier  150  and/or the inputs  162  and  164  of the third amplifier  160 . As shown in equation (2), the secondary resonance frequency can be set to a desired frequency by choosing the capacitance of the second capacitor  148  and the inductance of the second inductor  146  accordingly. 
     The coupling factor K depends on the overlap between the first inductor  144  and the second inductor  146 . For example, the first inductor  144  and the second inductor  146  may be integrated on a chip in which the first inductor  144  is implemented with a first planar loop inductor and the second inductor  146  is implemented with a second planar loop inductor on the chip. In this example, the first inductor  144  and the second inductor  146  are formed in different layers of the chip with the first inductor  144  overlapping the second inductor  146  to magnetically couple the first inductor  144  and the second inductor  146 . In this example, the coupling factor K is a function of the overlap between the first inductor  144  and the second inductor  146 , where the coupling factor K is larger for a larger overlap. Thus, the coupling factor K may be set to a desired value by laying out the first inductor  144  and the second inductor  146  on the chip such that the overlap between the first inductor  144  and the second inductor  146  corresponds to the desired coupling factor K. 
     As discussed above, the passband of the transformer  130  is a function of the primary resonance frequency, the secondary resonance frequency, and the coupling factor K. In one example, the center frequency of the passband is a function of the primary resonance frequency and the secondary resonance frequency of the transformer  130 . In this example, the primary resonance frequency and the secondary resonance frequency may each be set to a frequency approximately equal to the desired center frequency for the passband. As discussed above, the primary resonance frequency is set by the capacitance of the first capacitor  142  and the inductance of the first inductor  144 , and the secondary resonance frequency is set by the capacitance of the second capacitor  148  and the inductance of the second inductor  146 . 
     In the above example, the bandwidth of the passband (i.e., the width of the passband in frequency) is a function of the coupling factor K. Thus, the passband may be set to a desired bandwidth by setting the coupling factor K accordingly. As discussed above, the coupling factor K may be set by the overlap between the first inductor  144  and the second inductor  146 . 
     As discussed above, the first amplifier  120  is used to amplify signals in both the first frequency band and the second frequency band. In this regard, the primary resonance frequency, the secondary resonance frequency, and the coupling factor K are chosen to provide the transformer  130  with a wide passband covering both the first frequency band and the second frequency band. An example of this is illustrated in  FIG. 3 , which shows an exemplary passband  310  of the transformer  130 . In this example, the passband  310  has a wide bandwidth covering both the first frequency band (labeled “FB 1 ”) and the second frequency band (labeled “FB 2 ”). This allows the first amplifier  120  to provide high gain for both frequency bands. 
     In the example shown in  FIG. 3 , the first frequency band spans approximately 7.2 GHz to 8.7 GHz and the second frequency band spans approximately 10.8 GHz to 13.8 GHz. Thus, in this example, the passband  310  spans 7.2 GHz to 13.8 GHz to cover both frequency bands. However, it is to be appreciated that the first frequency band and the second frequency band are not limited to the above frequencies. 
     In some applications, the system  110  is used to amplify signals in one of the first frequency band and the second frequency band at a time. For example, in the first mode, the system  110  is used to amplify signals in the first frequency band, and, in the second mode, the system  110  is used to amplify signals in the second frequency band. In these applications, maintaining a wide passband that covers both frequency bands reduces the power efficiency of the first amplifier  120 . This is because only a portion of the wide passband is needed at a time since the first amplifier  120  amplifies signals in one of the frequency bands at a time. As a result, the wide passband causes the first amplifier  120  to consume power maintaining high gain for the frequency band that is not being used at a given time. The power efficiency is further reduced for the case where the first frequency band and the second frequency band are non-contiguous, as shown in the example in  FIG. 3 . This is because the wide passband covers frequencies in the frequency gap between the first frequency band and the second frequency band which causes the first amplifier  120  to consume power providing high gain within the frequency gap. 
     Aspects of the present disclosure increase the power efficiency of the first amplifier  120  by providing a switchable transformer configured to switch between a first passband and a second passband. In one example, the first passband covers the first frequency band and the second passband covers the second frequency band. In this example, each of the first and second passbands has a narrower bandwidth than the wide passband discussed above. In operation, a controller switches the switchable transformer to the first passband when the first frequency band is being used and switches the switchable transformer to the second passband when the second frequency band is being used. Thus, the controller switches the switchable transformer to one of the first and second passbands at a time depending on which of the first and second frequency bands is being used. Since one of the first and second passbands is used at a time and each of the first and second passbands has a narrower bandwidth than the wide passband discussed above, the power consumption of the first amplifier  120  is reduced, thereby increasing power efficiency. 
       FIG. 4A  shows an example of a system  405  in a transmitter according to certain aspects of the present disclosure. The system  405  is configured to amplify signals before the signals are transmitted via one or more antennas (not shown) coupled to the transmitter. In one example, the system  405  receives intermediate frequency (IF) signals from a previous stage (not shown) that converts baseband signals from a baseband processor into the IF signals. In this example, the system  405  amplifies the IF signals and outputs the amplified IF signals to a subsequent stage (not shown) that frequency upconverts the amplified IF signals into radio frequency (RF) signals for transmission. In other implementations, the system  405  may amplify RF signals. 
     In certain aspects, the system  405  is configured to amplify signals (e.g., IF signals) in multiple frequency bands. The multiple frequency bands may include the first frequency band and the second frequency band discussed above. 
     In the example in  FIG. 4A , the system  405  includes the first amplifier  120 , the second amplifier  150 , and the third amplifier  160  discussed above. The system  405  also includes a switchable transformer  410  configured to switch between a first passband and a second passband under the control of a controller  480 . In one example, the first passband covers the first frequency band and the second passband covers the second frequency band. As discussed further below, the controller  480  switches the switchable transformer  410  to the first passband in a first mode when the first frequency band is being used and switches the switchable transformer  410  to the second passband in a second mode when the second frequency band is being used. 
     The switchable transformer  410  has a primary side, a first secondary side, and a second secondary side. As discussed further below, the first secondary side is used for the first passband and the second secondary side is used for the second passband. In this example, the primary side includes a first switchable inductor  440  and a first capacitor  430  coupled in parallel with the first switchable inductor  440 . The first switchable inductor  440  is coupled between a first terminal  412  of the switchable transformer  410  and a second terminal  414  of the switchable transformer  410 . The first terminal  412  is coupled to the first output  126  of the first amplifier  120  and the second terminal  414  is coupled to the second output  128  of the first amplifier  120 . 
     The first switchable inductor  440  is configured to switch between a first primary inductance and a second primary inductance where the first primary inductance is used for the first passband and the second primary inductance is used for the second passband. In the example in  FIG. 4A , the first switchable inductor  440  includes a first inductor  442 , a second inductor  444 , a third inductor  446 , a fourth inductor  448 , and a switching circuit  455 . The first inductor  442  and the second inductor  444  are coupled in series between the first terminal  412  and the switching circuit  455 , and the third inductor  446  and the fourth inductor  448  are coupled in series between the second terminal  414  and the switching circuit  455 . The switching circuit  455  is also coupled between the first inductor  442  and the second inductor  444 , and between the third inductor  446  and the fourth inductor  448 . The switching circuit  455  is also coupled to a bias node  438 , which is biased by a DC voltage. 
     In operation, the switching circuit  455  switches the switchable inductor  440  between the first primary inductance in the first mode and the second primary inductance in the second mode under the control of the controller  480 . In the first mode, the switching circuit  455  couples the first inductor  442 , the second inductor  444 , the third inductor  446 , and the fourth inductor  448  in series between the first terminal  412  and the second terminal  414  (and hence between the first output  126  and the second output  128  of the first amplifier  120 ). In the first mode, the first primary inductance of the first switchable inductor  440  has an inductance equal to the sum of the inductances of the first inductor  442 , the second inductor  444 , the third inductor  446 , and the fourth inductor  448 . The switching circuit  455  may also couple the bias node  438  between the second inductor  444  and the third inductor  446  in which the bias node provides a common mode voltage for the differential signal at the differential output of the first amplifier  120 . 
     In the second mode, the switching circuit  455  couples the first inductor  442  and the fourth inductor  448  in series between the first terminal  412  and the second terminal  414  (and hence between the first output  126  and the second output  128  of the first amplifier  120 ). In the second mode, the switching circuit  455  bypasses the second inductor  444  and the third inductor  446 . Thus, the second inductor  444  and the third inductor  446  do not contribute to the inductance of the first switchable inductor  440  in the second mode. In the second mode, the second primary inductance of the first switchable inductor  440  has an inductance equal to the sum of the inductances of the first inductor  442  and the fourth inductor  448 . The switching circuit  455  may also couple the bias node  438  between the first inductor  442  and the fourth inductor  448 . 
     In the first mode, the first switchable inductor  440  has a first primary resonance given by following: 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁢ 
                     
                       r 
                       
                         p 
                         ⁢ 
                         1 
                       
                     
                   
                   = 
                   
                     1 
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                         
                           
                             C 
                             1 
                           
                           ⁢ 
                           
                             L 
                             
                               p 
                               ⁢ 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where fr p1  is the first primary resonance frequency, C 1  is the capacitance of the first capacitor  430 , and L p1  is the first primary inductance. C 1  may also include parasitic capacitance at the outputs  126  and  128  of the first amplifier  120 . In the second mode, the first switchable inductor  440  has a second primary resonance frequency given by the following: 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁢ 
                     
                       r 
                       
                         p 
                         ⁢ 
                         2 
                       
                     
                   
                   = 
                   
                     1 
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                         
                           
                             C 
                             1 
                           
                           ⁢ 
                           
                             L 
                             
                               p 
                               ⁢ 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     where fr p2  is the second primary resonance frequency and L p2  is the second primary inductance. Thus, the first switchable inductor  440  allows the primary side of the switchable transformer  410  to switch between a first primary resonance frequency in the first mode and a second primary resonance frequency in the second mode. 
     The first secondary side of the switchable transformer  410  includes a second switchable inductor  460  and a second capacitor  432  coupled in parallel with the second switchable inductor  460 . The second switchable inductor  460  is coupled between a third terminal  416  of the switchable transformer  410  and a fourth terminal  418  of the switchable transformer  410 . The third terminal  416  is coupled to the first input  152  of the second amplifier  150  (e.g., via one or more metal lines, a transmission line, or a combination thereof) and the fourth terminal  418  is coupled to the second input  154  of the second amplifier  150  (e.g., via one or more metal lines, a transmission line, or a combination thereof). The second switchable inductor  460  is magnetically coupled to the first switchable inductor  440  by a coupling factor K 1  which may depend on the overlap between the second switchable inductor  460  and the first switchable inductor  440 . 
     The second switchable inductor  460  includes a fifth inductor  462 , a sixth inductor  464 , and a switch  466  coupled between the fifth inductor  462  and the sixth inductor  464 . In the first mode, the controller  480  closes the switch  466 . Thus, in the first mode, the second switchable inductor  460  has an inductance given by the sum of the inductances of the fifth inductor  462  and the sixth inductor  464 . In the second mode, the controller  480  opens the switch  466 , which decouples the fifth inductor  462  and the sixth inductor  464 . This effectively disables the second switchable inductor  460 . 
     In the example shown in  FIG. 4A , the switch  466  is located at the center of the second switchable inductor  460 , which acts as a virtual ground for a differential signal at the second switchable inductor  460 . In this example, locating the switch  466  at the virtual ground significantly reduces the impact that the parasitic capacitance of the switch  466  has on the differential signal. However, it is to be appreciated that the present disclosure is not limited to this example. In other implementations, the switch  466  may be placed in another location in the second switchable inductor  460 , as discussed further below. 
     In the first mode, the second switchable inductor  460  has a first secondary resonance frequency given by the following: 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁢ 
                     
                       r 
                       
                         s 
                         ⁢ 
                         1 
                       
                     
                   
                   = 
                   
                     1 
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                         
                           
                             C 
                             2 
                           
                           ⁢ 
                           
                             L 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     where fr s1  is the first secondary resonance frequency, C 2  is the capacitance of the second capacitor  432 , and L 2  is the inductance of the second switchable inductor  460 . C 2  may also include parasitic capacitance at the inputs  152  and  154  of the second amplifier  150 . 
     The second secondary side of the switchable transformer  410  includes a third switchable inductor  470  and a third capacitor  434  coupled in parallel with the third switchable inductor  470 . The third switchable inductor  470  is coupled between a fifth terminal  420  of the switchable transformer  410  and a sixth terminal  422  of the switchable transformer  410 . The fifth terminal  420  is coupled to the first input  162  of the third amplifier  160  (e.g., via one or more metal lines, a transmission line, or a combination thereof) and the sixth terminal  422  is coupled to the second input  164  of the third amplifier  160  (e.g., via one or more metal lines, a transmission line, or a combination thereof). The third switchable inductor  470  is magnetically coupled to the first switchable inductor  440  by a coupling factor K 2  which may depend on the overlap between the third switchable inductor  470  and the first switchable inductor  440 . 
     The third switchable inductor  470  includes a seventh inductor  472 , an eighth inductor  474 , and a switch  476  coupled between the seventh inductor  472  and the eighth inductor  474 . In the first mode, the controller  480  opens the switch  476  which decouples the seventh inductor  472  and the eighth inductor  474 . This effectively disables the third switchable inductor  470 . In the second mode, the controller  480  closes the switch  476 . Thus, in the second mode, the third switchable inductor  470  has an inductance given by the sum of the inductances of the seventh inductor  472  and the eighth inductor  474 . 
     In the example shown in  FIG. 4A , the switch  476  is located at the center of the third switchable inductor  470 , which acts as a virtual ground for a differential signal at the third switchable inductor  470 . In this example, locating the switch  476  at the virtual ground significantly reduces the impact that the parasitic capacitance of the switch  476  has on the differential signal. However, it is to be appreciated that the present disclosure is not limited to this example. In other implementations, the switch  476  may be placed in another location in the third switchable inductor  470 , as discussed further below. 
     In the second mode, the third switchable inductor  470  has a second secondary resonance frequency given by the following: 
     
       
         
           
             
               
                 
                   
                     f 
                     ⁢ 
                     
                       r 
                       
                         s 
                         ⁢ 
                         2 
                       
                     
                   
                   = 
                   
                     1 
                     
                       2 
                       ⁢ 
                       π 
                       ⁢ 
                       
                         
                           
                             C 
                             3 
                           
                           ⁢ 
                           
                             L 
                             3 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     where fr s2  is the second secondary resonance frequency, C 3  is the capacitance of the third capacitor  434 , and L 3  is the inductance of the third switchable inductor  470 . C 3  may also include parasitic capacitance at the inputs  162  and  164  of the third amplifier  160 . 
     As discussed above, the controller  480  switches the switchable transformer  410  to the first mode when the first frequency band is being used. In the first mode, the switchable transformer  410  has a first passband that is a function of the first primary resonance fr p1  given in equation (3), the first secondary resonance frequency fr s1  given in equation (5), and the first coupling factor K 1  discussed above. In certain aspects, the first passband is configured to cover the first frequency band by setting the first primary resonance fr p1 , the first secondary resonance frequency fr s1 , and the first coupling factor K 1  accordingly. An example of the first passband  510  is shown in  FIG. 5A . In this example, the first passband  510  covers the first frequency band (labeled “FB 1 ”) and therefore provides high gain for the first frequency band. In addition, the first passband  510  has a narrower bandwidth than the wide passband  310  shown in  FIG. 3 , and therefore reduces power consumption of the first amplifier  120 . 
     In the second mode, the switchable transformer  410  has a second passband that is a function of the second primary resonance fr p2  given in equation (4), the second secondary resonance frequency fr s2  given in equation (6), and the second coupling factor K 2  discussed above. In certain aspects, the second passband is configured to cover the second frequency band by setting the second primary resonance fr p2 , the second secondary resonance frequency fr s2 , and the second coupling factor K 2  accordingly. An example of the second passband  520  is shown in  FIG. 5B . In this example, the second passband  520  covers the second frequency band (labeled “FB 2 ”) and therefore provides high gain for the second frequency band. In addition, the second passband  520  has a narrower bandwidth than the wide passband  310  shown in  FIG. 3 , and therefore reduces power consumption of the first amplifier  120 . 
     Each of the capacitors  430 ,  432 , and  434  may be implemented with a variable capacitor (shown in the example in  FIG. 4A ) or a fixed capacitor. For example, the first capacitor  430  may be implemented with a variable capacitor to finely tune the resonance frequency of the primary side of the switchable transformer  410  (e.g., to compensate for process-voltage-temperature (PVT) variation). Similarly, the second capacitor  432  may be implemented with a variable capacitor to finely tune the resonance frequency of the first secondary side of the switchable transformer  410  (e.g., to compensate for PVT variation), and the third capacitor  434  may be implemented with a variable capacitor to finely tune the resonance frequency of the second secondary side of the switchable transformer  410  (e.g., to compensate for PVT variation). 
     In some implementations, the inputs  152  and  154  of the second amplifier  150  may be DC biased through a center tap of the second switchable inductor  460 . In other implementations, the inputs  152  and  154  of the second amplifier  150  may be DC biased by a separate DC bias voltage source (not shown) (e.g., for the case where the inputs  152  and  154  of the second amplifier  150  are coupled to the switchable transformer  410  via long transmission lines). In this example, the system  405  may include coupling capacitors between the inputs  152  and  154  of the second amplifier  150  and the switchable transformer  410  to isolate the DC bias voltage at the inputs  152  and  154  of the second amplifier  150  from the switchable transformer  410 . In this regard,  FIG. 4B  shows an example of a first coupling capacitor  482  coupled between the first input  152  of the second amplifier  150  and the third terminal  416  of the switchable transformer  410 , and a second coupling capacitor  484  coupled between the second input  154  of the second amplifier  150  and the fourth terminal  418  of the switchable transformer  410 . 
     In some implementations, the inputs  162  and  164  of the third amplifier  160  may be DC biased through a center tap of the third switchable inductor  470 . In other implementations, the inputs  162  and  164  of the third amplifier  160  may be DC biased by a separate DC bias voltage source (not shown) (e.g., for the case where the inputs  162  and  164  of the third amplifier  160  are coupled to the switchable transformer  410  via long transmission lines). In this example, the system  405  may include coupling capacitors between the inputs  162  and  164  of the third amplifier  160  and the switchable transformer  410  to isolate the DC bias voltage at the inputs  162  and  164  of the third amplifier  160  from the switchable transformer  410 . In this regard,  FIG. 4B  shows an example of a third coupling capacitor  486  coupled between the first input  162  of the third amplifier  160  and the fifth terminal  420  of the switchable transformer  410 , and a fourth coupling capacitor  488  coupled between the second input  164  of the third amplifier  160  and the sixth terminal  422  of the switchable transformer  410 . 
       FIG. 4C  shows another exemplary implementation of the second switchable inductor  460  and the third switchable inductor  470 . In this example, the second switchable inductor  460  includes an inductor  492 , a first switch  466 - 1  coupled between the inductor  492  and the third terminal  416  and a second switch  466 - 2  coupled between the inductor  492  and the fourth terminal  418 . In the first mode, the controller  480  closes the switches  466 - 1  and  466 - 2  and, in the second mode, the controller  480  opens the switches  466 - 1  and  466 - 2 . However, it is to be appreciated that the second switchable inductor  460  is not limited to the exemplary implementations shown in  FIGS. 4A and 4C . In general, the second switchable inductor  460  includes at least one inductor and at least one switch coupled in series with the at least one inductor in which the second switchable inductor  460  is enabled when the at least one switch is closed and disabled with the at least one switch is open. In the examples in  FIGS. 4A and 4C , the second capacitor  432  is coupled in parallel with the at least one inductor and the at least one switch. 
     In this example, the third switchable inductor  470  includes an inductor  494 , a first switch  476 - 1  coupled between the inductor  494  and the fifth terminal  420  and a second switch  476 - 2  coupled between the inductor  494  and the sixth terminal  422 . In the first mode, the controller  480  opens the switches  476 - 1  and  476 - 2  and, in the second mode, the controller  480  closes the switches  476 - 1  and  476 - 2 . However, it is to be appreciated that the third switchable inductor  470  is not limited to the exemplary implementations shown in  FIGS. 4A and 4C . In general, the third switchable inductor  470  includes at least one inductor and at least one switch coupled in series with the at least one inductor in which the third switchable inductor  470  is enabled when the at least one switch is closed and disabled with the at least one switch is open. In the examples in  FIGS. 4A and 4C , the third capacitor  434  is coupled in parallel with the at least one inductor and the at least one switch. 
       FIG. 6  shows an exemplary implementation of the switching circuit  455 . In this example, the switching circuit  455  includes a first switch  610  coupled between the second inductor  444  and the bias node  438 , and a second switch  615  coupled between the third inductor  446  and the bias node  438 . The switching circuit  455  also includes a third switch  620  coupled between the first inductor  442  and the bias node, and a fourth switch  625  coupled between the fourth inductor  448  and the bias node  438 . 
     In the first mode, the controller  480  closes the first switch  610  and the second switch  615 , and opens the third switch  620  and the fourth switch  625 . As a result, the first inductor  442 , the second inductor  444 , the third inductor  446 , and the fourth inductor  448  coupled in series between the first terminal  412  and the second terminal  414 . In this mode, the primary side has the first primary inductance discussed above which is equal to the sum of the inductances of the first inductor  442 , the second inductor  444 , the third inductor  446 , and the fourth inductor  448 . 
     In the second mode, the controller  480  opens the first switch  610  and the second switch  615 , and closes the third switch  620  and the fourth switch  625 . As a result, the first inductor  442  and the fourth inductor  448  are coupled in series between the first terminal  412  and the second terminal  414 . In this mode, the primary side has the second primary inductance discussed above which is equal to the sum of the inductances of the first inductor  442  and the fourth inductor  448 . 
     In the example shown in  FIG. 6 , the switches  610 ,  615 ,  620 , and  625  are located adjacent to the center of the first switchable inductor  440 , which acts as a virtual ground for a differential signal at the first switchable inductor  440 . In this example, locating the switches  610 ,  615 ,  620 , and  625  adjacent to the virtual ground significantly reduces the impact that the parasitic capacitances of the switches  610 ,  615 ,  620 , and  625  have on the differential signal. 
     It is to be appreciated that the switching circuit  455  is not limited to the exemplary implementation shown in  FIG. 6 . In this regard, it is to be appreciated that the exemplary functions of the switching circuit  455  discussed above may be realized using other arrangements of switches. 
     It is also to be appreciated that the first switchable inductor  440  is not limited to the exemplary implementation shown in  FIG. 6 . In this regard, it is to be appreciated that the first switchable inductor  440  may be implemented with other arrangements of two or more inductors and one or more switches configured to switch the first switchable inductor  440  between the first primary inductance and the second primary inductance. In general, the first switchable inductor  440  may include at least one first inductor (e.g., inductors  442  and  448 ), at least one second inductor (e.g., inductors  444  and  446 ) coupled in series with the at least one first inductor, and at least one switch (e.g., switches  620  and  625 ) coupled in parallel with the at least one second inductor. In general, the first switchable inductor  440  may be switched to the first primary inductance by opening the at least one switch, in which the first primary inductance is equal to the sum of the inductances of the at least one first inductor and the at least one second inductor. The first switchable inductor  440  may be switched to the second primary inductance by closing the at least one switch, in which the second primary inductance is equal to the inductance of the at least one first inductor. In this case, the at least one second inductor is bypassed. In general, the first capacitor  430  is coupled in parallel with the at least one first inductor and the at least one second inductor. 
       FIG. 7A  shows a top view of an example of an inductor  710  that may be used to implement the first inductor  442 , the second inductor  444 , the third inductor  446 , and the fourth inductor  448 . However, it is to be appreciated that the present disclosure is not limited to this example, and that the first inductor  442 , the second inductor  444 , the third inductor  446 , and the fourth inductor  448  may be implemented with another inductor. 
     In this example, the inductor  710  is a planar spiral inductor integrated on a chip. The inductor  710  may be formed from a first metal layer on the chip using photolithography and/or another fabrication technique. The different portions of the inductor  710  corresponding to the first inductor  442 , the second inductor  444 , the third inductor  446 , and the fourth inductor  448  are labeled in  FIG. 7A  according to certain aspects. In the example in  FIG. 7A , ends  722  and  728  of the inductor  710  are coupled by a bridge  760  (shown in  FIG. 7B ) that crosses over portion  726  of the inductor  710 . The bridge  760  is formed from a different metal layer than the first metal layer discussed above, and allows one portion of the inductor  710  to cross over another portion of the inductor  710  for the example where the inductor  710  is a spiral inductor. Each end  722  and  728  of the inductor  710  may be coupled to the bridge  760  by a respective via (not shown). It is to be appreciated that, in some implementations, the bridge  760  may cross under portion  726  of the inductor  710 . Similarly, ends  740  and  742  of the inductor  710  are coupled by a bridge  765  (shown in  FIG. 7B ) that crosses over portion  746  of the inductor  710 . 
     In this example, the switching circuit  455  (not shown in  FIG. 7A ) is coupled between locations  724  and  722  of the inductor  710 , and between locations  732  and  734  of the inductor  710 . Location  724  corresponds to the terminal of the first inductor  442  coupled to the second inductor  444 , and location  722  corresponds to the terminal of the fourth inductor  448  coupled to the third inductor  446 . In the second mode, the switching circuit  455  couples the inductor  710  to the bias node  438  (not shown in  FIG. 7A ) at locations  724  and  722 . In this case, the inductance of the first switchable inductor  440  is approximately equal to the sum of the inductances of the first inductor  442  and the fourth inductor  448 . 
     Location  732  corresponds to the terminal of the second inductor  444  coupled to the switching circuit  455 , and location  734  corresponds to the terminal of the third inductor  446  coupled to the switching circuit  455 . In this example, locations  732  and  734  of the inductor  710  correspond to two ends of the inductor  710  separated by a gap. In the first mode, the switching circuit  455  couples the inductor  710  to the bias node  438  at locations  732  and  734 . In this case, the inductance of the first switchable inductor  440  is approximately equal to the sum of the inductances of the first inductor  442 , the second inductor  444 , the third inductor  446 , and the fourth inductor  448 . 
       FIG. 8A  shows a top view of an example of an inductor  810  that may be used to implement the fifth inductor  462  and the sixth inductor  464 . However, it is to be appreciated that the present disclosure is not limited to this example, and that the fifth inductor  462  and the sixth inductor  464  may be implemented with another inductor. 
     In this example, the inductor  810  is a planar spiral inductor integrated on a chip. The inductor  810  may be formed from a second metal layer on the chip using photolithography and/or another fabrication technique. The different portions of the inductor  810  corresponding to the fifth inductor  462  and the sixth inductor  464  are labeled in  FIG. 8A  according to certain aspects. In the example in  FIG. 8A , ends  820  and  822  of the inductor  810  are coupled by a bridge  850  (shown in  FIG. 8B ) that crosses over portion  824  of the inductor  810 . The bridge  850  is formed from a different metal layer than the second metal layer discussed above, and allows one portion of the inductor  810  to cross over another portion of the inductor  810  for the example where the inductor  810  is a spiral inductor. Each end  820  and  822  of the inductor  810  may be coupled to the bridge  850  by a respective via (not shown). It is to be appreciated that, in some implementations, the bridge  850  may cross under portion  824  of the inductor  810 . 
     In this example, the switch  466  (not shown in  FIG. 8A ) is coupled between locations  812  and  814  of the inductor  810 . Location  812  corresponds to the terminal of the sixth inductor  464  coupled to the switch  466 , and location  814  corresponds to the terminal of the fifth inductor  462  coupled to the switch  466 . The controller  480  (not shown in  FIG. 8A ) turns on the switch  466  in the first mode and turns off the switch  466  in the second mode. 
       FIG. 9  shows a top view of an example of an inductor  910  that may be used to implement the seventh inductor  472  and the eighth inductor  474 . However, it is to be appreciated that the present disclosure is not limited to this example, and that the seventh inductor  472  and the eighth inductor  474  may be implemented with another inductor. 
     In this example, the inductor  910  is a planar loop inductor. The inductor  910  may be formed from a third metal layer on the chip using photolithography and/or another fabrication technique. The different portions of the inductor  910  corresponding to the seventh inductor  472  and the eighth inductor  474  are labeled in  FIG. 9  according to certain aspects. 
     In this example, the switch  476  (not shown in  FIG. 9 ) is coupled between locations  912  and  914  of the inductor  910 . Location  912  corresponds to the terminal of the seventh inductor  472  coupled to the switch  476 , and location  914  corresponds to the terminal of the eighth inductor  474  coupled to the switch  476 . The controller  480  (not shown in  FIG. 9 ) turns off the switch  476  in the first mode and turns on the switch  476  in the second mode. 
       FIG. 10  shows a top view of the inductors  710 ,  810 , and  910  according to certain aspects. 
     In this example, the inductor  810  overlaps the inductor  710  to provide magnetic coupling of the inductors  710  and  810 , and the inductor  910  overlaps the inductor  710  to provide magnetic coupling of the inductors  710  and  910 . The overlapping of the inductors  710 ,  810 , and  910  is possible since the inductors  710 ,  810 , and  910  are formed from different metal layers on the chip. More particularly, the inductor  710  is formed from the first metal layer of the chip, the inductor  810  is formed from the second metal layer of the chip, and the inductor  910  is formed from the third metal layer of the chip. In the example in  FIG. 10 , the inductor  810  is located below the inductor  710 , and the inductor  910  is located above the inductor  710 . However, it is to be appreciated that the present disclosure is not limited to this example. In another implementation, the inductor  810  may be located above the inductor  710 , and the inductor  910  may be located below the inductor  710 . 
     The degree of overlap between the inductor  710  and the inductor  810  determines the coupling factor K 1  between the primary side and the first secondary side of the switchable transformer  410 . Thus, in this example, a desired coupling factor K 1  between the primary side and the first secondary side can be achieved by laying out the inductors  710  and  810  such that the overlap between the inductors  710  and  810  corresponds to the desired coupling factor K 1 . 
     Similarly, the degree of overlap between the inductor  710  and the inductor  910  determines the coupling factor K 2  between the primary side and the second secondary side of the switchable transformer  410 . Thus, in this example, a desired coupling factor K 2  between the primary side and the second secondary side can be achieved by laying out the inductors  710  and  910  such that the overlap between the inductors  710  and  910  corresponds to the desired coupling factor K 2 . 
     It is to be appreciated that the terms “first metal layer,” “second metal layer,” and “third metal layer” are used herein as a convenient way of distinguishing between the different metal layers used to form the inductors  810 ,  710 , and  910 . In certain aspects, the first metal layer, the second metal, and the third metal layer may include the top three metal layers of a chip to minimize parasitic capacitances. However, it is to be appreciated that the first metal layer, the second metal layer, and the third metal layer are not limited to this example. 
       FIG. 11  shows an example of a system  1105  in a transmitter according to certain aspects. The system  1105  includes the exemplary system  405  illustrated in any one of  FIGS. 4A  to  4 C. The system  1105  also includes a first transformer  1110 , a second transformer  1135 , a first mixer  1155 , a third transformer  1160 , and a second mixer  1180 . 
     In the example in  FIG. 11 , the primary side of the first transformer  1110  includes a first inductor  1115  and a capacitor  1125  coupled in parallel between ground and a first terminal  1112  of the first transformer  1110 . The secondary side of the first transformer  1110  includes a second inductor  1120  and a resistor  1130  coupled in parallel between a second terminal  1124  and a third terminal  1126  of the first transformer  1110 . The first inductor  1115  and the second inductor  1120  are magnetically coupled (i.e., inductively coupled). 
     In this example, the first terminal  1112  of the first transformer  1110  is coupled to a previous stage (not shown) of the transmitter. The previous stage may receive a baseband signal (e.g. from a baseband processor), convert the baseband signal into an IF signal, and input the IF signal to the first terminal  1112  of the first transformer  1110 . The differential input of the first amplifier  120  is coupled to the secondary side of the first transformer  1110 . More particularly, the second terminal  1124  of the first transformer  1110  is coupled to the first input  122  of the first amplifier  120  and the third terminal  1126  of the first transformer  1110  is coupled to the second input  124  of the first amplifier  120 . The first amplifier  120  may have parasitic capacitance at the inputs  122  and  124  in which the resonance frequency at the secondary side of the first transformer  1110  is determined by the inductance of the second inductor  1120  and the parasitic capacitance. 
     In this example, the first transformer  1110  is configured to have a passband covering the first frequency band and the second frequency band so that signals in both frequency bands are passed to the first amplifier  120 . In this regard, the inductances of the first and second inductors  1115  and  1120 , the capacitance of the capacitor  1125 , and the coupling factor K between the first and second inductors  1115  and  1120  are chosen to achieve a passband covering the first and second frequency bands. The resistor  1130  may be used for de-Qing at the differential input of the first amplifier  120 . In this example, the first transformer  1110  may also be configured to convert a single-ended IF signal received at the first terminal  1112  into a differential IF signal at the second and third terminals  1124  and  1126 . 
     In the example in  FIG. 11 , the primary side of the second transformer  1135  includes a first inductor  1140  and a first capacitor  1144  coupled in parallel between a first terminal  1136  of the second transformer  1135  and a second terminal  1138  of the second transformer  1135 . The secondary side of the second transformer  1135  includes a second inductor  1142  and a second capacitor  1146  coupled in parallel between a third terminal  1150  and a fourth terminal  1152  of the second transformer  1135 . The first inductor  1140  and the second inductor  1142  are magnetically coupled (i.e., inductively coupled). 
     In this example, the second amplifier  150  has a differential output including a first output  1132  coupled to the first terminal  1136  of the second transformer  1135 , and a second output  1134  coupled to the second terminal  1138  of the second transformer  1135 . The third terminal  1150  and the fourth terminal  1152  of the second transformer  1135  are coupled to the first mixer  1155 . 
     In this example, the second transformer  1135  is configured to have a passband covering the first frequency band so that second amplifier  150  amplifies signals in the first frequency band. In this regard, the inductances of the first and second inductors  1140  and  1142 , the capacitances of the first and second capacitors  1144  and  1146 , and the coupling factor K between the first and second inductors  1140  and  1142  are chosen to achieve a passband covering the first frequency band. 
     The first mixer  1155  is configured to receive the amplified signal in the first frequency band from the second transformer  1135  and frequency upconvert the signal into an RF signal for transmission. The first mixer  1155  may upconvert the signal by mixing the signal with a first local oscillator signal. 
     In the example in  FIG. 11 , the primary side of the third transformer  1160  includes a first inductor  1165  and a first capacitor  1170  coupled in parallel between a first terminal  1162  of the third transformer  1160  and a second terminal  1164  of the third transformer  1160 . The secondary side of the third transformer  1160  includes a second inductor  1168  and a second capacitor  1172  coupled in parallel between a third terminal  1176  and a fourth terminal  1178  of the third transformer  1160 . The first inductor  1165  and the second inductor  1168  are magnetically coupled (i.e., inductively coupled). 
     In this example, the third amplifier  160  has a differential output including a first output  1156  coupled to the first terminal  1162  of the third transformer  1160 , and a second output  1158  coupled to the second terminal  1164  of the third transformer  1160 . The third terminal  1176  and the fourth terminal  1178  of the third transformer  1160  are coupled to the second mixer  1180 . 
     In this example, the third transformer  1160  is configured to have a passband covering the second frequency band so that third amplifier  160  amplifies signals in the second frequency band. In this regard, the inductances of the first and second inductors  1165  and  1168 , the capacitances of the first and second capacitors  1170  and  1172 , and the coupling factor K between the first and second inductors  1165  and  1168  are chosen to achieve a passband covering the second frequency band. 
     The second mixer  1180  is configured to receive the amplified signal in the second frequency band from the third transformer  1160  and frequency upconvert the signal into an RF signal for transmission. The second mixer  1180  may upconvert the signal by mixing the signal with a second local oscillator signal. 
     Each of the capacitors  1125 ,  1144 ,  1146 ,  1170 , and  1172  may be implemented with a variable capacitor (shown in the example in  FIG. 11 ) or a fixed capacitor. 
       FIG. 12  shows an example in which the transmitter includes a power amplifier  1210  and an antenna  1225 . The input of the power amplifier  1210  is coupled to the output of the first mixer  155  and the output of the power amplifier  1210  is coupled to the antenna  1225 . The input of the first mixer  1155  is coupled to the second transformer  1135  shown in  FIG. 11 . In operation, the power amplifier  1210  is configured to receive the RF signal output by the first mixer  1155 , amplify the RF signal, and output the amplified RF signal to the antenna  1225  for transmission. It is to be appreciated that the transmitter may include one or more additional components between the first mixer  1155  and the antenna  1225  not shown in  FIG. 12 . 
       FIG. 13  shows an example in which the transmitter includes a splitter  1310 , an antenna array  1340  including multiple antennas  1325 - 1  to  1325 - n , and multiple transmit chains  1312 - 1  to  1312 - n  according to certain aspects. The splitter  1310  has an input coupled to the output of the first mixer  1155  and multiple outputs. Each transmit chain  1312 - 1  to  1312 - n  is coupled between a respective one of the outputs of the splitter  1310  and a respective one of the antennas  1325 - 1  to  1325 - n.    
     In this example, each of the transmit chains  1312 - 1  to  1312 - n  includes a respective phase shifter  1315 - 1  to  1315 - n  and a respective power amplifier  1320 - 1  to  1320 - n . In each transmit chain  1312 - 1  to  1312 - n , the input of the respective phase shifter  1315 - 1  to  1315 - n  is coupled to the respective output of the splitter  1310 , the input of the respective power amplifier  1320 - 1  to  1320 - n  is coupled to the output of the respective phase shifter  1315 - 1  to  1315 - n , and the output of the respective power amplifier  1320 - 1  to  1320 - n  is coupled to the respective antenna  1325 - 1  to  1325 - n . Each phase shifter  1315 - 1  to  1315 - n  is configured to shift the phase of the respective RF signal by a respective phase. Each power amplifier  1320 - 1  to  1320 - n  is configured to amplify the signal from the respective phase shifter  1315 - 1  to  1315 - n  and output the amplified signal to the respective antenna  1325 - 1  to  1325 - n  for transmission. In operation, a beamformer (not shown) controls the phases of the phase shifters  1315 - 1  to  1315 - n  to achieve a desired transmit beam direction for the antenna array  1340  using beamforming. 
       FIG. 14  shows an example in which the transmitter includes a power amplifier  1410  and an antenna  1425 . The input of the power amplifier  1410  is coupled to the output of the second mixer  1180  and the output of the power amplifier  1410  is coupled to the antenna  1425 . The input of the second mixer  1180  is coupled to the third transformer  1160  shown in  FIG. 11 . In operation, the power amplifier  1410  is configured to receive the RF signal output by the second mixer  1180 , amplify the RF signal, and output the amplified RF signal to the antenna  1425  for transmission. It is to be appreciated that the transmitter may include one or more additional components between the second mixer  1180  and the antenna  1425  not shown in  FIG. 14 . 
       FIG. 15  shows an example in which the transmitter includes a splitter  1510 , an antenna array  1540  including multiple antennas  1525 - 1  to  1525 - n , and multiple transmit chains  1512 - 1  to  1512 - n  according to certain aspects. The splitter  1510  has an input coupled to the output of the second mixer  1180  and multiple outputs. Each transmit chain  1512 - 1  to  1512 - n  is coupled between a respective one of the outputs of the splitter  1510  and a respective one of the antennas  1525 - 1  to  1525 - n.    
     In this example, each of the transmit chains  1512 - 1  to  1512 - n  includes a respective phase shifter  1515 - 1  to  1515 - n  and a respective power amplifier  1520 - 1  to  1520 - n . In each transmit chain  1512 - 1  to  1512 - n , the input of the respective phase shifter  1515 - 1  to  1515 - n  is coupled to the respective output of the splitter  1510 , the input of the respective power amplifier  1520 - 1  to  1520 - n  is coupled to the output of the respective phase shifter  1515 - 1  to  1515 - n , and the output of the respective power amplifier  1520 - 1  to  1520 - n  is coupled to the respective antenna  1525 - 1  to  1525 - n . Each phase shifter  1515 - 1  to  1515 - n  is configured to shift the phase of the respective RF signal by a respective phase. Each power amplifier  1520 - 1  to  1520 - n  is configured to amplify the signal from the respective phase shifter  1515 - 1  to  1515 - n  and output the amplified signal to the respective antenna  1525 - 1  to  1525 - n  for transmission. In operation, a beamformer (not shown) controls the phases of the phase shifters  1515 - 1  to  1515 - n  to achieve a desired transmit beam direction for the antenna array  1540  using beamforming. 
       FIG. 16  is a diagram of an environment  1600  that includes an electronic device  1602  that includes a wireless transceiver  1696 . The wireless transceiver  1696  may include the any one or more of the systems illustrated in  FIGS. 4A, 4B, 4C, 6, and 11 to 15 . In the environment  1600 , the electronic device  1602  communicates with a base station  1604  through a wireless link  1606 . As shown, the electronic device  1602  is depicted as a smart phone. However, the electronic device  1602  may be implemented as any suitable computing or other electronic device, such as a cellular base station, broadband router, access point, cellular or mobile phone, gaming device, navigation device, media device, laptop computer, desktop computer, tablet computer, server computer, network-attached storage (NAS) device, smart appliance, vehicle-based communication system, Internet of Things (IoT) device, sensor or security device, asset tracker, and so forth. 
     The base station  1604  communicates with the electronic device  1602  via the wireless link  1606 , which may be implemented as any suitable type of wireless link. Although depicted as a base station tower of a cellular radio network, the base station  1604  may represent or be implemented as another device, such as a satellite, terrestrial broadcast tower, access point, peer to peer device, mesh network node, fiber optic line, another electronic device generally as described above, and so forth. Hence, the electronic device  1602  may communicate with the base station  1604  or another device via a wired connection, a wireless connection, or a combination thereof. The wireless link  1606  can include a downlink of data or control information communicated from the base station  1604  to the electronic device  1602  and an uplink of other data or control information communicated from the electronic device  1602  to the base station  1604 . The wireless link  1606  may be implemented using any suitable communication protocol or standard, such as 3rd Generation Partnership Project Long-Term Evolution ( 3GPP LTE, 3GPP NR 5G), IEEE 802.11, IEEE 802.16, Bluetooth™, and so forth. 
     The electronic device  1602  includes a processor  1680  and a memory  1682 . The memory  1682  may be or form a portion of a computer readable storage medium. The processor  1680  may include any type of processor, such as an application processor or a multi-core processor, that is configured to execute processor-executable instructions (e.g., code) stored by the memory  1682 . The memory  1682  may include any suitable type of data storage media, such as volatile memory (e.g., random access memory (RAM)), non-volatile memory (e.g., Flash memory), optical media, magnetic media (e.g., disk or tape), and so forth. In the context of this disclosure, the memory  1682  is implemented to store instructions  1684 , data  1686 , and other information of the electronic device  1602 , and thus when configured as or part of a computer readable storage medium, the memory  1682  does not include transitory propagating signals or carrier waves. 
     The electronic device  1602  may also include input/output (I/O) ports  1690 . The I/O ports  1690  enable data exchanges or interaction with other devices, networks, or users or between components of the device. 
     The electronic device  1602  may further include a signal processor (SP)  1692  (e.g., such as a digital signal processor (DSP)). The signal processor  1692  may function similar to the processor and may be capable executing instructions and/or processing information in conjunction with the memory  1682 . 
     For communication purposes, the electronic device  1602  also includes a modem  1694 , the wireless transceiver  1696 , and one or more antennas (e.g., the antenna  1225 , the antenna  1425 , the antenna array  1340  and/or the antenna array  1540 ). The wireless transceiver  1696  provides connectivity to respective networks and other electronic devices connected therewith using RF wireless signals. The wireless transceiver  1696  may facilitate communication over any suitable type of wireless network, such as a wireless local area network (LAN) (WLAN), a peer to peer (P2P) network, a mesh network, a cellular network, a wireless wide area network (WWAN), a navigational network (e.g., the Global Positioning System (GPS) of North America or another Global Navigation Satellite System (GNSS)), and/or a wireless personal area network (WPAN). 
     The controller  480  may be implemented with a general-purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete hardware components (e.g., logic gates), or any combination thereof designed to perform the functions described herein. A processor may perform the functions described herein by executing software comprising code for performing the functions. The software may be stored on a computer-readable storage medium, such as a RAM, a ROM, an EEPROM, an optical disk, and/or a magnetic disk. 
       FIG. 17  illustrates a method  1700  for operating an apparatus according to certain aspects. The apparatus includes a first amplifier (e.g., first amplifier  120 ), and a transformer (e.g., switchable transformer  410 ) including a first switchable inductor (e.g., first switchable inductor  440 ) coupled to the first amplifier, a second switchable inductor (e.g., second switchable inductor  460 ) magnetically coupled to the first switchable inductor, and a third switchable inductor (e.g., third switchable inductor  470 ) magnetically coupled to the first switchable inductor. 
     At block  1710 , in a first mode, the first switchable inductor is switched to a first inductance. For example, the first switchable inductor may be switched to the first inductance by the switching circuit  455 . 
     At block  1720 , in the first mode, the second switchable inductor is enabled. For example, the second switchable inductor may be enabled by closing the switch  466 . In this example, the switch  466  may be closed by the controller  480 . 
     At block  1730 , in the first mode, the third switchable inductor is disabled. For example, the third switchable inductor may be disabled by opening the switch  476 . In this example, the switch  476  may be opened by the controller  480 . 
     At block  1740 , in a second mode, the first switchable inductor is switched to a second inductance. For example, the first switchable inductor may be switched to the second inductance by the switching circuit  455 . 
     At block  1750 , in the second mode, the second switchable inductor is disabled. For example, the second switchable inductor may be disabled by opening the switch  466 . In this example, the switch  466  may be opened by the controller  480 . 
     At block  1760 , in the second mode, the third switchable inductor is enabled. For example, the third switchable inductor may be enabled by closing the switch  476 . In this example, the switch  476  may be closed by the controller  480 . 
     Implementation examples are described in the following numbered clauses: 
     1. An apparatus, comprising:
         a first amplifier having a first output and a second output;   a transformer comprising:
           a first switchable inductor coupled between the first output and the second output;   a first capacitor coupled in parallel with the first switchable inductor;   a second switchable inductor magnetically coupled to the first switchable inductor;   a second capacitor coupled in parallel with the second switchable inductor;   a third switchable inductor magnetically coupled to the first switchable inductor; and   a third capacitor coupled in parallel with the third switchable inductor.   
               

     2. The apparatus of clause 1, further comprising:
         a second amplifier coupled to the second switchable inductor; and   a third amplifier coupled to the third switchable inductor.       

     3. The apparatus of clause 2, wherein the second amplifier has a first input and a second input, and the second switchable inductor is coupled between the first input of the second amplifier and the second input of the second amplifier. 
     4. The apparatus of clause 2 or 3, further comprising a mixer coupled to an output of the second amplifier. 
     5. The apparatus of clause 4, further comprising a power amplifier coupled to the mixer. 
     6. The apparatus of any one of clauses 2 to 5, wherein the third amplifier has a first input and a second input, and the third switchable inductor is coupled between the first input of the third amplifier and the second input of the third amplifier. 
     7. The apparatus of any one of clauses 1 to 6, wherein the first switchable inductor is switchable between a first inductance and a second inductance. 
     8. The apparatus of clause 7, wherein the second switchable inductor comprises:
         at least one inductor; and   at least one switch coupled in series with the at least one inductor.       

     9. The apparatus of clause 8, further comprising a controller configured to:
         in a first mode, switch the first switchable inductor to the first inductance and close the at least one switch; and   in a second mode, switch the first switchable inductor to the second inductance and open the at least one switch.       

     10. The apparatus of clause 8 or 9, further comprising a second amplifier having a first input and a second input, wherein the second switchable inductor is coupled between the first input of the second amplifier and the second input of the second amplifier. 
     11. The apparatus of clause 7, wherein:
         the second switchable inductor comprises:
           at least one first inductor; and   at least one first switch coupled in series with the at least one first inductor; and   
           the third switchable inductor comprises:
           at least one second inductor; and   at least one second switch coupled in series with the at least one second inductor.   
               

     12. The apparatus of clause 11, further comprising a controller configured to:
         in a first mode, switch the first switchable inductor to the first inductance, close the at least one first switch, and open the at least one second switch; and   in a second mode, switch the first switchable inductor to the second inductance, open the at least one first switch, and close the at least one second switch.       

     13. The apparatus of clause 11 or 12, further comprising:
         a second amplifier having a first input and a second input, wherein the second switchable inductor is coupled between the first input of the second amplifier and the second input of the second amplifier; and   a third amplifier having a first input and a second input, wherein the third switchable inductor is coupled between the first input of the third amplifier and the second input of the third amplifier.       

     14. The apparatus of any one of clauses 1 to 6, wherein the first switchable inductor comprises:
         a first inductor;   a second inductor;   a third inductor;   a fourth inductor; and   a switching circuit, wherein the switching circuit is configured to:
           couple the first inductor, the second inductor, the third inductor, and the fourth inductor in series between the first output of the first amplifier and the second output of the first amplifier; and   couple the first inductor and the fourth inductor in series between the first output of the first amplifier and the second output of the first amplifier.   
               

     15. The apparatus of clause 14, wherein the second switchable inductor comprises:
         a fifth inductor;   a sixth inductor; and   a first switch coupled between the fifth inductor and the sixth inductor.       

     16. The apparatus of clause 15, further comprising a second amplifier having a first input and a second input, wherein the second switchable inductor is coupled between the first input of the second amplifier and the second input of the second amplifier. 
     17. The apparatus of clause 15 or 16, wherein the third switchable inductor comprises:
         a seventh inductor;   an eighth inductor; and   a second switch coupled between the seventh inductor and the eighth inductor.       

     18. The apparatus of clause 15 or 17, further comprising:
         a second amplifier having a first input and a second input, wherein the second switchable inductor is coupled between the first input of the second amplifier and the second input of the second amplifier; and   a third amplifier having a first input and a second input, wherein the third switchable inductor is coupled between the first input of the third amplifier and the second input of the third amplifier.       

     19. A method for operating an apparatus, wherein the apparatus includes a first amplifier, and a transformer including a first switchable inductor coupled to the first amplifier, a second switchable inductor magnetically coupled to the first switchable inductor, and a third switchable inductor magnetically coupled to the first switchable inductor, the method comprising:
         in a first mode,
           switching the first switchable inductor to a first inductance;   enabling the second switchable inductor; and   disabling the third switchable inductor;   
           in a second mode,
           switching the first switchable inductor to a second inductance;   disabling the second switchable inductor; and   enabling the third switchable inductor.   
               

     20. The method of clause 19, where the apparatus further comprises:
         a second amplifier coupled to the second switchable inductor; and   a third amplifier coupled to the third switchable inductor.       

     21. The method of clause 20, further comprising:
         amplifying a first signal in a frequency band and a second signal in a second frequency band using the first amplifier;   amplifying the first signal in the first frequency band using the second amplifier; and   amplifying the second signal in the second frequency band using the third amplifier.       

     22. The method of any one of clauses 19 to 21, wherein:
         the second switchable inductor includes:
           at least one first inductor; and   at least one first switch coupled in series with the at least one first inductor;   
           enabling the second switchable inductor comprises closing the at least one first switch; and   disabling the second switchable inductor comprises opening the at least one first switch.       

     23. The method of clause 22, wherein:
         the third switchable inductor includes:
           at least one second inductor; and   at least one second switch coupled in series with the at least one second inductor;   
           enabling the third switchable inductor comprises closing the at least one second switch; and   disabling the third switchable inductor comprises opening the at least one second switch.       

     24. The method of any one of clauses 19 to 21, wherein:
         the first switchable inductor comprises:
           at least one first inductor;   at least one second inductor; and   at least one switch coupled in parallel with the at least one second inductor;   
           switching the first switchable inductor to the first inductance comprises opening the at least one switch; and   switching the second switchable inductor to the second inductance comprises closing the at least one switch.       

     25. The method of any one of clauses 19 to 24, wherein the apparatus further includes:
         a first capacitor coupled in parallel with the first switchable inductor;   a second capacitor coupled in parallel with the second switchable inductor; and   a third capacitor coupled in parallel with the third switchable inductor.       

     26. An apparatus, comprising:
         a first amplifier having a first output and a second output;   a transformer comprising:
           at least one first inductor;   at least one second inductor, wherein the at least one first inductor and the at least one second inductor are coupled between the first output and the second output of the first amplifier;   at least one first switch coupled in parallel with the at least one second inductor;   at least one third inductor magnetically coupled to the at least one first inductor and the at least one second inductor;   at least one second switch coupled in series with the at least one third inductor;   a second capacitor coupled in parallel with the at least one third inductor and the at least one second switch;   at least one fourth inductor magnetically coupled to the at least one first inductor;   at least one third switch coupled in series with the at least one fourth inductor; and   a third capacitor coupled in parallel with the at least one fourth inductor and the at least one third switch.   
               

     27. The apparatus of clause 26, further comprising a second amplifier having a first input and a second input, wherein the at least one third inductor and the at least one second switch are coupled in series between the first input of the second amplifier and the second input of the second amplifier. 
     28. The apparatus of clause 27, further comprising a third amplifier having a first input and a second input, wherein the at least one fourth inductor and the at least one third switch are coupled in series between the first input of the third amplifier and the second input of the third amplifier. 
     29. The method of clause 23, wherein:
         the first switchable inductor comprises:
           at least one third inductor;   at least one fourth inductor; and   at least one third switch coupled in parallel with the at least one fourth inductor;   
           switching the first switchable inductor to the first inductance comprises opening the at least one third switch; and   switching the second switchable inductor to the second inductance comprises closing the at least one third switch.       

     It is to be appreciated that the present disclosure is not limited to the exemplary terminology used above to describe aspects of the present disclosure. For example, an inductor of a transformer may also be referred to as a winding or another term. Also, it is to be appreciated that an inductor may be referred to as a coil even in cases where the inductor is not physically implemented with a coil. It is also to be appreciated that magnetic coupling may also be referred to as inductive coupling or another term. 
     It is to be appreciated that any of the switches discussed above may be implemented with one or more n-type field effect transistors (NFETs), one or more p-type field effect transistors (PFETs), a transmission gate, or another type of switch. For an example of a switch implemented with an NFET, the switch is turned on by applying a high voltage (e.g., supply voltage) to the gate of the NFET and turned off by applying a low voltage (e.g., ground) to the gate of the NFET. For an example of a switch implemented with a PFET, the switch is turned off by applying a high voltage (e.g., supply voltage) to the gate of the PFET and turned on by applying a low voltage (e.g., ground) to the gate of the PFET. 
     Within the present disclosure, the word “exemplary” is used to mean “serving as an example, instance, or illustration.” Any implementation or aspect described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects of the disclosure. Likewise, the term “aspects” does not require that all aspects of the disclosure include the discussed feature, advantage or mode of operation. The term “coupled” is used herein to refer to the direct or indirect electrical coupling between two structures. It is also to be appreciated that the term “ground” may refer to a DC ground or an AC ground, and thus the term “ground” covers both possibilities. It is also to be appreciated that an “inductor” may include multiple inductors coupled in series. It is also to be appreciated than an “input” may be a single-ended input, a differential input, or one of two inputs of a differential input, and an “output” may be a single-ended output, a differential output, or one of two outputs of a differential output. 
     The previous description of the disclosure is provided to enable any person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other variations without departing from the spirit or scope of the disclosure. Thus, the disclosure is not intended to be limited to the examples described herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.