Patent Publication Number: US-2022224295-A1

Title: Methods and apparatus for power amplifier transformers

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This patent application claims the benefit of and priority to U.S. Provisional Patent Application Ser. No. 63/136,485 filed Jan. 12, 2021, which is hereby incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     This description relates generally to transformers, and more particularly to methods and apparatus for power amplifier transformers. 
     BACKGROUND 
     Some electronic devices include one or more transceivers to communicate with other devices using radio frequency (RF) signals. Such transceivers include RF power amplifiers to convert low-power RF signals corresponding to data to a higher power signal that drives an antenna of the transceiver to transmit the data to other devices. Such RF power amplifiers may include matching networks to create a matched impedance between an input stage and a modulator, between an output stage and the input stage, and between a load (such as an antenna) and the output stage. 
     SUMMARY 
     For methods and apparatus for power amplifier transformers, an example apparatus includes a first transformer winding. The first transformer winding includes a first proximal end and a first distal end. The example apparatus includes a second transformer winding. The second transformer winding includes a second proximal end and a second distal end, the first proximal end having a first distance from the second proximal end and the first distal end having a second distance from the second distal end, the first distance less than the second distance. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of an example power amplifier including an example split-combine transformer for coupling and impedance matching. 
         FIG. 2  is a first schematic diagram of the example split-combine transformer of  FIG. 1  for coupling and impedance matching. 
         FIG. 3  is a second schematic diagram of the example split-combine transformer of  FIG. 1  for coupling and impedance matching. 
         FIG. 4  is a third schematic diagram of the example split-combine transformer of  FIG. 1  for coupling and impedance matching. 
         FIG. 5  is a graph of output power of the example power amplifier of  FIG. 1  with respect to operating frequency of the example power amplifier of  FIG. 1 . 
     
    
    
     DETAILED DESCRIPTION 
     The drawings are not necessarily to scale. Generally, the same reference numbers in the drawing(s) and this description refer to the same or like parts. Although the drawings show layers and regions with clean lines and boundaries, some or all of these lines and/or boundaries may be idealized. In reality, the boundaries and/or lines may be unobservable, blended and/or irregular. 
     A power amplifier is a last stage in a radio frequency (RF) transmitter and is used to amplify a signal level so that the RF transmitter can deliver a required output power to an antenna. The RF transmitter may be a part of a radar system, a communication system, and/or any type of wireless system. In a radar system application, the system may operate at a high level of frequency (such as 77 Gigahertz (GHz)). In such an example, the power amplifier (PA) must be designed to deliver 15 dBm-17 dBm (such as approximately 50 milliwatts (mW)). Power amplifiers use large devices to deliver such output power and improve output power with high efficiency. Especially switching power amplifiers, which use significantly large devices (such as large MOSFETs) to reduce switching on resistance. However, driving the PA devices becomes harder and harder with increased device size due to large parasitic capacitances induced by the larger devices. For example, parasitic capacitance may be introduced by the MOSFET devices in the matching network, between the stages of a driver (such as circuitry that drives and/or facilitates operation of the PA) and the PA stage. In some examples, smaller matching components are needed to compensate for this parasitic capacitance. 
     In some examples, a transformer is provided between the driver stage and the PA stage for implementing the matching network. The transformer may include of two inductors magnetically coupled to each other. The transformer includes a primary stage and a secondary stage. In this example, the primary stage may be coupled to an output of the driver, which may be smaller in size than the PA. The secondary stage is coupled to the primary stage and to the PA. The driver, being smaller than the PA, has a smaller parasitic capacitance. The parasitic capacitances are resonated, by the driver and PA, at the operating frequency of the radar system and, thus, the primary side of the transformer requires a bigger inductance than the secondary side of the transformer, because a larger capacitance exists in the secondary side which needs to be resonated, so a smaller inductance is needed to resonate the larger capacitance. 
     When designing the transformer for the PA, the transformer is to include a large turn ratio, such that a primary coil includes a greater inductance than a secondary coil to ensure that there is a smaller secondary inductance at the PA input. However, quality factor (such as an indication of a performance of the transformer) and coefficient of coupling (such as a fraction of magnetic flux produced by current in one coil that links with the other coil) of the transformer degrades with increased turn ratio and reduced coil size, which limits a signal swing at the PA input and, thus, degrades the output power and efficiency. All of these limitations are exacerbated with increased operating frequency (e.g. at millimeter-wave frequencies). 
     Previous solutions addressed the problem of poor quality factor and coefficient of coupling of the transformer by implementing power combiners. Power combiners can facilitate a high turn ratio without sacrificing quality factor and coefficient of coupling by splitting last stage into multiple paths, thus avoiding large device capacitances Power combiners, also referred to as power splitters, split the input signal into multiple paths, amplify the split input signals separately, and use series or parallel combiners at the output. Some power combiners, however, are designed to have multiple lead lines (such as excessive routing) depending on the type of PA that the transformers are providing a signal to. At high frequencies, excessive routing in a power combining system results in unwanted (such as parasitic) losses. In some examples, power combiners have high loss due to the splitting process sharing the same signal between a number of outputs, which degrades the overall PA output power and efficiency. Therefore, a need exists for a transformer that includes a minimal amount of connections and optimizes an operation of the PA in high operating frequency systems. 
     Examples described herein improve the efficiency of power combiners and, thus, improves the efficiency of PA operation and output power. Examples described herein implement a split and combine transformer, having secondary windings angled relative to a central axis, that includes a higher primary inductance and a lower secondary inductance. The transformer described herein is made up of two transformers, where two secondary windings of the transformers both have the same inductance as two primary windings (such as a 1:1 ratio between primary side and secondary side). The two primary windings are connected in series and the two secondary windings are connected in parallel. The parallel connection of the two secondary windings reduces the inductance of the secondary side and, thus, the transformer has a higher primary inductance and a lower secondary inductance. Rather than having one smaller winding in the secondary side of the transformer, two large windings are connected in parallel to avoid a degrading of quality factor and coupling coefficient. In some examples, the split and combine transformer may split and combine k coils, such that a number of primary windings may differ from a number of secondary windings. In such an example, the number of secondary windings have a combined number of turns equal to a combined number of turns of the number of primary windings, such that the turn ratio of the split and combine transformer is still 1:1. 
     In examples described herein, the transformers are angled at from a central axis that extends between the transformers and bisects the outputs of the transformers. For example, the transformer extends from the central axis at a first angle and a second transformer extends from the central axis at a second angle. The outputs of the transformers are located at respective proximal ends of the transformers and center taps of the transformers are located at respective distal ends of the transformers. A distance between the proximal ends is less than a distance between the distal ends and, thus, the outputs are closer to the central axis than the center taps. Such angling of transformers shortens the routing at the output of the transformers which improves the parasitic inductance of the transformer. 
     As used herein, the terms “coefficient of coupling” and “coupling coefficient” are defined as a value that indicates the efficiency of transferring power from one side of a transformer coil to the other side of the transformer coil. For example, when current flows through one coil (such as the primary coil), the current produces flux (such as magnetic flux). The whole flux may not link with the other coil (such as the secondary coil) connected to the one coil (such as the primary coil) because of leakage flux, which is denoted by a fraction (k). The fraction (k) is the coupling coefficient. When the coupling coefficient is equal to one (1), the flux produced by one coil completely links with the other coil and is magnetically tightly connected to the other coil. When the coupling coefficient is equal to zero (0), the flux produced by one coil does not link at all with the other coil and, thus, the coils are said to be magnetically isolated. 
     As used herein, “routing” and/or “track” are terms used to refer to a wiring structure of a printed circuit board (PCB). The term “routing” may refer to a single wiring structure (such as a single wire coupling two components) and/or multiple wiring structures (such as more than one wire coupling two or more components). 
     As used herein, “power added efficiency,” “PAE,” and/or “linearity” are metrics for rating power amplifiers. PAE and/or linearity can be metrics by which customers determine which power amplifiers to purchase. For example, power amplifiers with a PAE below a certain level may not be purchased by a customer due to the impact of PAE on a customer product. A lower PAE can, for example, reduce the battery life of an electronic device, such as a mobile phone. However, enhancing PAE can come at the cost of reducing linearity. Similarly, increasing linearity can cause a decrease in PAE. In some examples, PAE is measured as a percentage. 
       FIG. 1  is a schematic diagram of an example power amplifier (PA)  100  including an example split-combine transformer  102  for coupling a driver stage  104  to an output stage  106  and for providing impedance matching between the driver stage  104  and the output stage  106 . The example PA  100  further includes an example input matching network  108  and an example output network  110 . 
     In  FIG. 1 , the example input matching network  108  includes a first input node  112  and a second input node  114  that receive and/or are configured to receive an input voltage (Vin)  116 . The input voltage (Vin)  116  is an RF signal that is positive at the first input node  112  relative to the second input node  114 , wherein the second input node can be a ground node and/or any other reference voltage connection. The input matching network  108  includes an example first transformer (T 1 )  118  having an example first transformer (T 1 ) primary winding  120  coupled between the first input node  112  and the second input node  114 , and an example first transformer (T 1 ) secondary winding  122 . The first transformer (T 1 )  118  is connected as a parallel resonant device using an example input capacitor  124 . In some examples, the first transformer (T 1 )  118  provides impedance transformation and isolation between the input  116  and the driver stage  104 . 
     In  FIG. 1 , the example input matching network  108  is coupled to a first biasing circuit  126   a . In some examples, the first biasing circuit  126   a  is a DC biasing circuit. The first biasing circuit  126   a  provides a DC biasing voltage to the driver stage  104 . The first biasing circuit  126   a  includes an example first resistor  128   a  that is coupled to a center tap of the T 1  secondary winding  122 , an example first capacitor  130   a  coupled to the first resistor  128   a , an example second resistor  132   a  coupled to the first capacitor  130   a  and the first resistor  128   a , an example first transistor  134   a , and an example third resistor  136   a . The first transistor  134   a  includes an emitter terminal, a collector terminal, and a base terminal (such as a control terminal, a current terminal, etc.). The collector terminal of the first transistor  124   a  is coupled to the third resistor  136   a  and configured to receive and/or obtain a first bias voltage (V B1 ). The base terminal of the first transistor  134   a  is coupled to second resistor  132   a , which is coupled to the collector terminal of the first transistor  134   a.    
     In  FIG. 1 , the example driver stage  104  includes an example second transistor  138   a , an example third transistor  138   b , an example second capacitor  140   a , and an example third capacitor  140   b . In this example, the second and third transistors  138   a ,  138   b  are NPN bipolar junction transistors (BJTs). Additionally and/or alternatively, the second and third transistors  138   a ,  138   b  may be implemented by n-channel metal-oxide-semiconductor field-effect transistors (NFETs), PNP BJTs, and/or any other type of transistor by reconfiguring the components of the driver stage  104 . The second transistor  138   a  includes an emitter terminal (such as a source terminal, a current terminal, etc.), a collector terminal (such as a drain terminal, a current terminal, etc.), and a base terminal (such as a control terminal, a current terminal, etc.). The third transistor  138   b  includes an emitter terminal (such as a source terminal, a current terminal, etc.), a collector terminal (such as a drain terminal, a current terminal, etc.), and a base terminal (such as a control terminal, a current terminal, etc.). The second capacitor  140   a  includes a first capacitor terminal and a second capacitor terminal. The third capacitor  140   b  includes a third capacitor terminal and a fourth capacitor terminal. 
     The base terminal of the second transistor  138   a  is coupled to a first output of the T 1  secondary winding  122  and the base terminal of the third transistor  138   b  is coupled to a second output of the T 1  secondary winding  122 . In some examples, the first output of the T 1  secondary winding  122  is a positive side of the winding  122  and the second output of the T 1  secondary winding  122  is a ground, reference, and/or negative side of the winding  122 . The first capacitor terminal of the second capacitor  140   a  is coupled to the first output of the T 1  secondary winding  122  and to the base terminal of the second transistor  138   a . The second capacitor terminal of the second capacitor  140   a  is coupled to the collector terminal of the third transistor  138   b . The third capacitor terminal of the third capacitor  140   b  is connected to the second output of the T 1  secondary winding  122  and to the base terminal of the third transistor  138   b . The fourth capacitor terminal of the third capacitor  140   b  is coupled to the collector terminal of the second transistor  138   a.    
     The second and third transistors  138   a ,  138   b  comprise a common-emitter differential amplifier to amplify a current generated by the first transformer  118 . The example second capacitor  140   a  and the example third capacitor  140   b  provide capacitive cross-coupling neutralization in the driver stage  104 . Capacitive neutralization improves the problem of low reverse isolation in power amplifiers with large transistor devices. For example, the transistors  138   a ,  138   b  in the driver stage  104  may be large and, thus, the parasitic gate-to-drain and/or base-to-collector capacitances of the transistors  138   a ,  138   b  are also large. Such parasitic base-to-collector capacitance lowers the reverse isolation, as well as power gain and stability of the power amplifier  100 . Cross-coupling capacitors  140   a ,  140   b  between base and collector of the respective opposite-side transistor cancels the parasitic base-to-emitter capacitance and improves reverse isolation. As used herein, reverse isolation is a measure of how well a signal applicated at an output of the power amplifier  100  is “isolated” from the input nodes  112 ,  114 . 
     In  FIG. 1 , the split-combine transformer  102  is an inter-stage matching network between the driver stage  104  and last stage devices (such as output stage  106 ). The split-combine transformer  102  includes a second transformer (T 2 )  142  and a third transformer (T 3 )  144 . The second transformer (T 2 )  142  includes a second transformer (T 2 ) primary winding  146  and a second transformer (T 2 ) secondary winding  148 . The third transformer (T 3 )  144  includes a third transformer (T 3 ) primary winding  150  and a third transformer (T 3 ) secondary winding  152 . The T 2  primary winding  146  includes a first input and a second input. The T 2  secondary winding  148  includes a first output and a second output. The T 3  primary winding  150  includes a third input and a fourth input. The T 3  secondary winding  152  includes a third output and a fourth output. The T 2  primary winding  146  and the T 3  primary winding  150  are connected in series and the T 2  secondary winding  148  and the T 3  secondary winding  152  are connected in parallel. 
     For example, the first input of the T 2  primary winding  146  is connected to the collector terminal of the second transistor  138   a  and the second input of the T 2  primary winding  146  is connected to the third input of the T 3  primary winding  150 . A supply voltage (V CC1 ) is provided at the second input and the third input of the primary windings  146 ,  150 . The first output of the T 2  secondary winding  148  is connected to the third output of the T 3  secondary winding  152  at a first node  103 A and the second output of the T 2  secondary winding  148  is connected to the fourth output of the T 3  secondary winding  152  at a second node  103 B. Similarly, the third output of T 3  secondary winding  152  is connected to the first output of T 2  secondary winding  148  and the fourth output of the T 3  secondary winding  152  is connected to the first output of the T 2  secondary winding  148 . In some examples, the split-combine transformer  102  is implemented by complimentary metal-oxide semiconductors (CMOS) compatible stacked-type on-chip transformers. Additionally and/or alternatively, the split-combine transformer  102  may be implemented by any type of on-chip transformers. 
     In some examples, the split-combine transformer  102  is a power combiner to increase the input signal (such as the input current from the driver stage  104 ) at the output. However, the power combiner (such as the split-combine transformer  102 ) does not use a high turn ratio in order to achieve the increase and/or amplification of the input signal. Instead, the power combiner (such as the split-combine transformer  102 ) comprises two transformers  142 ,  144 , where a sum of the secondary winding turns is equal to a sum of primary winding turns. For example, the turn ratio of the second transformer (T 2 )  142  is 1:1 and the turn ratio of the third transformer (T 3 )  144  is 1:1. The second transformer (T 2 )  142  and the third transformer (T 3 )  144  may include any combination of primary windings and secondary windings, and the sum of the secondary winding turns will always be equal to the sum of the primary winding turns. For example, if the second transformer (T 2 )  142  includes two secondary windings and one primary winding and the third transformer (T 3 )  144  includes two secondary windings and one primary winding, a sum of the turns of the four secondary windings is equal to a sum of the turns of the two primary windings. In this manner, the split-combine transformer  102  comprises a 1:1 turn ratio. 
     The split-combine transformer  102  is able to amplify and/or increase the input signal at the output, without having a high turn ratio, due to the parallel connection of the secondary windings  148 ,  152 . For example, the current of the first output of the T 2  secondary winding  148  and the current of the third output of the T 3  secondary winding  152  are combined and injected into a base terminal of a first output stage transistor (such as fifth transistor  154   a ). In another example, the current of the second output of the T 2  secondary winding  148  and the current of the fourth output of the T 3  secondary winding  152  are combined and injected into a base terminal of a second output stage transistor (such as sixth transistor  154   b ) at 180 degree phase difference from the current injected into the base terminal of the first output stage transistor (such as fifth transistor  154   a ). As such, the parallel connection of the secondary windings  148  and  152  put high base currents into the output stage transistors (such as fifth and sixth transistors  154   a ,  154   b ). The split-combine transformer  102  of  FIG. 1  is described in further detail below in connection with  FIGS. 2, 3, and 4 . 
     In  FIG. 1 , the example split-combine transformer  102  is connected to a second biasing circuit  126   b . In some examples, the second biasing circuit  126   b  is a DC biasing circuit. The second biasing circuit  126   b  provides a DC biasing voltage to the output stage  106 . The second biasing circuit  126   b  includes an example fourth resistor  128   b  that is coupled to a center tap of the T 2  secondary winding  148 , an example fifth resistor  128   c  that is coupled to a center tap of the T 3  secondary winding  152 , an example sixth resistor  132   b  coupled to the fourth resistor  128   b  and to the fifth resistor  128   c , an example fourth transistor  134   b , and an example seventh resistor  136   b . The fourth transistor  134   b  includes an emitter terminal, a collector terminal, and a base terminal (such as a control terminal, a current terminal, etc.). The collector terminal of the fourth transistor  134   b  is coupled to the seventh resistor  136   b  and configured to receive and/or obtain a second bias voltage (V B2 ). The base terminal of the fourth transistor  134   b  is coupled to sixth resistor  132   b , which is coupled to the collector terminal of the fourth transistor  134   b.    
     In  FIG. 1 , the output stage  106  includes an example fifth transistor  154   a , an example sixth transistor  154   b , an example fifth capacitor  156   a , and an example sixth capacitor  156   b . In this example, the fifth and sixth transistors  154   a ,  154   b  are NPN bipolar junction transistors (BJTs). Additionally and/or alternatively, the fifth and sixth transistors  154   a ,  154   b  may be implemented by n-channel metal-oxide-semiconductor field-effect transistors (NFETs), PNP BJTs, and/or any other type of transistor by reconfiguring the components of the output stage  106 . The fifth transistor  154   a  includes an emitter terminal (such as a source terminal, a current terminal, etc.), a collector terminal (such as a drain terminal, a current terminal, etc.), and a base terminal (such as a control terminal, a current terminal, etc.). The sixth transistor  154   b  includes an emitter terminal (such as a source terminal, a current terminal, etc.), a collector terminal (such as a drain terminal, a current terminal, etc.), and a base terminal (such as a control terminal, a current terminal, etc.). The fifth capacitor  156   a  includes a fifth capacitor terminal and a sixth capacitor terminal. The sixth capacitor  156   b  includes a seventh capacitor terminal and an eighth capacitor terminal. 
     The base terminal of the fifth transistor  154   a  is connected to the first output of the T 2  secondary winding  148  and to the third output of the T 3  secondary winding  152 . The base terminal of the sixth transistor  154   b  is connected to the second output of the T 2  secondary winding  148  and to the fourth output of the T 3  secondary winding  152 . The fifth capacitor terminal of the fifth capacitor  156   a  is connected to the first output of the T 2  secondary winding  148 , to the third output of the T 3  secondary winding  152 , and to the base terminal of the fifth transistor  154   a . The sixth capacitor terminal of the fifth capacitor  156   a  is coupled to the collector terminal of the sixth transistor  154   b . The seventh capacitor terminal of the sixth capacitor  156   b  is connected to the second output of the T 2  secondary winding  148 , to the fourth output of the T 3  secondary winding  152 , and to the base terminal of the sixth transistor  154   b . The eighth capacitor terminal of the sixth capacitor  156   b  is coupled to the collector terminal of the fifth transistor  154   a.    
     The fifth and sixth transistors  154   a ,  154   b  comprise a common-emitter differential amplifier to amplify a power at the output of the split-combine transformer  102 . The example fifth capacitor  156   a  and the example sixth capacitor  156   b  provide capacitive cross-coupling neutralization in the output stage  106 . The example output stage  106  is to provide power gain between the driver stage  104  and a load. The power gain is to have high input impedance and low output impedance. 
     In  FIG. 1 , the example output network  110  includes a fourth transformer (T 4 )  158 , a fifth transformer (T 5 )  160 , and an output capacitor  170 . The fourth transformer (T 4 )  158  includes a fourth transformer (T 4 ) primary winding  162  and a fourth transformer (T 4 ) secondary winding  164 . The fifth transformer (T 5 )  160  includes a fifth transformer (T 5 ) primary winding  166  and a fifth transformer (T 5 ) secondary winding  168 . The T 4  primary winding  162  includes a fifth input and a sixth input and the T 4  secondary winding  164  includes a fifth output and a sixth output. The T 5  primary winding  166  includes a seventh input and an eighth input and the T 5  secondary winding  168  includes a seventh output and an eighth output. 
     In  FIG. 1 , the example output capacitor  170  is connected between the secondary windings of the fourth transformer  158  and the fifth transformer  160 . For example, the output capacitor  170  is connected between the fifth output of the T 4  secondary winding  164  and the eighth output of the T 5  secondary winding  168 . The fifth input of the T 4  primary winding  162  is connected to the collector terminal of the fifth transistor  154   a  and the sixth input of the T 4  primary winding  162  is connected to a second supply voltage (VCC 2 ). The seventh input of the T 5  primary winding  166  is connected to the second supply voltage (VCC 2 ) and the eighth input of the T 5  primary winding  166  is connected to the collector terminal of the sixth transistor  154   b . The secondary windings  164 ,  168  are connected to a load, such as a filter, an antenna, etc. 
     In an example operation of the power amplifier  100  of  FIG. 1 , the driver stage  104  receives an input signal (such as Vin)  116  having a particular center frequency. In some examples, the power amplifier  100  is applicable to various operating frequencies. Accordingly, components of the power amplifier  100  may be different for different operating frequencies and/or frequency ranges. For example, the center frequency may in a first frequency range greater than 76 GHz and/or in a second frequency range less than 81 GHz. The example driver stage  104  amplifies the input voltage  116  to generate an amplified output signal  101  (such as  101   a  and  101   b ). 
     The split-combine transformer  102  is provided to match an impedance between the output of the driver stage  104  and an input of the output stage  106 . The split-combine transformer  102  achieves an impedance transformation between the input of the split-combine transformer  102  and the output of the split-combine transformer  102 , while maintaining transformation efficiency, due to the sum of primary winding turns equaling the sum of secondary windings turns. 
     For example, the desired impedance transformation corresponds to a desire for the power amplifier  100  to achieve high power delivery (such as transferring power in the amplified output signal  101  from the driver stage  104  to the output stage  106 ) while meeting any device requirements (such as requirements of the device implemented the power amplifier  100 , such as low supply voltages). To achieve high power delivery at the power amplifier output, an inter-stage matching network, such as the split-combine transformer  102 , is to include a low output impedance when transferring the power from the driver stage  104  to the output stage  106 . In some example, a high transformation ratio is implemented to ensure a low output impedance, which can lower efficiency of that inter-stage matching network due to power loss between primary and secondary windings having different numbers of coils. Additionally, low output impedance is associated with high sensitivity to parasitic capacitances and/or resistances. However, the split-combine transformer  102  does not lose as much power between primary and secondary windings because the turn ratio of the split-combine transformer  102  is equal (such as 1:1) and, thus, the split-combine transformer  102  is efficient while achieving low output impedance. 
     In the example operation of the power amplifier  100 , the power from the driver stage  104  is transferred to the output stage  106 . The output stage  106  further amplifies the power using the common-emitter differential amplifier (such as the fifth and sixth transistors  154   a ,  154   b ). The example output network  110  is provided to match an impedance between the output stage  106  and a load (not illustrated). 
       FIG. 2  is a schematic diagram of the example split-combine transformer  102  of  FIG. 1  to provide impedance matching between an output (such as the driver stage  104 ) and an input (such as the input of the output stage  106 ) while efficiently increasing power of an input signal (such as Vin  116 ). The example schematic diagram of  FIG. 2  illustrates all metallization layers (layers of conductive materials, such as metals, dielectrics, resin, etc.) of the split-combine transformer  102 . For example, the schematic diagram of  FIG. 2  is a final implementation of the split-combine transformer  102 , including the signal paths, the devices, and any other layers of the split-combine transformer  102 . As used herein out, the schematic diagram of  FIG. 2  is a first schematic diagram  200  of the split-combine transformer  102  of  FIG. 1 . 
     In  FIG. 2 , the example first schematic diagram  200  includes the example second transformer (T 2 )  142  and the example third transformer (T 3 )  144 . The example first schematic diagram  200  includes example supply voltage decoupling capacitors  202 , example bias circuitry inputs  204 A,  204 B, and example bias decoupling capacitors  206 . 
     In  FIG. 2 , the example second transformer (T 2 )  142  includes the example T 2  primary winding  146  and the example T 2  secondary winding  148 . In the first schematic diagram  200 , the T 2  primary winding  146  comprises a first layer of material (such as a first metallization layer) shaded with diagonal lines and the T 2  secondary winding  148  comprises a second layer of material (such as a second metallization layer) shaded with dots. In  FIG. 2 , the example third transformer (T 3 )  144  includes the example T 3  primary winding  150  and the example T 3  secondary winding  152 . Similarly to the T 2  primary winding and the T 2  secondary winding, the T 3  primary winding  150  comprises a first layer of material (such as the first metallization layer), shaded with diagonal lines and the T 3  secondary winding  152  comprises the second layer of material (such as the second metallization layer), shaded with dots. 
     In  FIG. 2 , the example supply voltage decoupling capacitors (decaps)  202  are connected to and/or coupled between the first supply voltage (V CC1 ) (not illustrated) and the ground. The example supply voltage decaps  202  are depicted as a third layer of material, shaded with vertical lines. In  FIG. 2 , the example bias circuitry outputs  204 A and  204 B are coupled, respectively, to center taps  208 A and  208 B of the T 2  and T 3  secondary windings  148 ,  152 . For example, a first bias circuitry output  204 A is coupled to a first center tap  208 A of the T 2  secondary winding  148 . In this example, a second bias circuitry output  204 B is coupled to a second center tap  208 B of the T 3  secondary winding  152 . In  FIG. 2 , the example bias decaps  206  are connected to and/or coupled between the bias circuitry outputs  204 A,  204 B and ground (such as coupled between the resistors  128   b ,  128   c ,  132   b  and ground). 
     In  FIG. 2 , the T 2  primary winding  146  is connected to the T 3  primary winding  150  in series and the T 2  secondary winding  148  is connected to the T 3  secondary winding  152  in parallel.  FIG. 3  illustrates the series and parallel connections of the second and third transformer  142 ,  144 . 
     In  FIG. 2 , the T 2  primary winding  146  and the T 3  primary winding  150  include an example primary center tap  210 . The primary center tap  210  comprises the second metallization layer, shaded by the dots. The example primary center tap  210  enables second (2 nd ) harmonic termination in the split-combine transformer  102 . In some examples, harmonic termination is used to tune and/or adjust an output (such as output waveform) of a power amplifier (such as power amplifier  100 ) by adding or removing some harmonic content. Therefore, the example primary center tap  210  may be coupled to a balancing and/or tuning network that is to achieve a tuning of the output at the second harmonic. In this example, a trace  212  (such as a signal trace) comprising of the second metallization layer, is coupled to the primary center tap  210 . In some examples, setting the width of the trace  212  tunes the 2 nd  harmonic frequency. The example primary center tap  210  is located at a more accessible point in the split-combine transformer  102  relative to a transformer in a conventional power combiner. 
       FIG. 3  is an example second schematic diagram  300  of the split-combine transformer  102  of  FIGS. 1 and 2 . The second schematic diagram  300  illustrates two layers (such as metallization layers) of the split-combine transformer  102 . The first layer corresponds to the T 2  primary winding  146  and the T 3  primary winding  150  and is depicted by the diagonal lines. The second layer corresponds to the T 2  secondary winding  148  and the T 3  secondary winding  152  and is depicted by the dots. 
     In the illustrated example of  FIG. 3 , the second transformer (T 2 )  142  includes a first output  302 A, a second output  302 B, and the first center tap  208 A. The third transformer (T 3 )  144  includes a third output  304 A, a fourth output  304 B, and the second center tap  208 B. In this example, the outputs  302 A,  302 B,  304 A,  304 B are outputs of transformer windings. For example, the first and second outputs  302 A,  302 B are T 2  secondary winding outputs and the third and fourth outputs  304 A,  304 B are T 3  secondary winding outputs. As mentioned above, the secondary winding outputs are coupled and/or connected in parallel. In this example, the first output  302 A is coupled and/or connected to the third output  304 A at a first node  103 A. The second output  302 B is coupled to and/or connected to the fourth output  304 B at the second node  103 B. The output at the first node  103 A and the output at the second node  103 B are 180 degrees out-of-phase. 
     In the illustrated example of  FIG. 3 , the second transformer (T 2 )  142  extends outward from an example central axis  301  of the second schematic diagram  300  at a first angle  303 A and the third transformer (T 3 )  144  extends outward from the example central axis  301  of the second schematic diagram  300  at a second angle  303 B. In the illustrated example of  FIG. 3 , the central axis  301  is a longitudinal axis (such as an axis parallel to a direction of outputs of the split-combine transformer  102 , inputs of the split-combine transformer  102 , etc.). For example, the central axis  301  extends between the second transformer  142  and the third transformer  144  and bisects a first split-combine output  306 A and a second split-combine output  306 B of the third transformer  144 . In the illustrated example of  FIG. 3 , the split-combine transformer  102  is symmetric about the central axis  301 . In other examples, the split-combine transformer  102  is asymmetric about the central axis  301 . In the illustrated example of  FIG. 3 , both of the angles  303 A,  303 B are 45°. In other examples, the angles  303 A,  303 B can have any other suitable value (such as 20°, 30°, 60°, etc.). In some examples, the first angle  303 A and the second angle  303 B can have different values (such as the first angle  303 A is 45° and the second angle  303 B 30°, etc.). 
     In the illustrated example of  FIG. 3 , the second transformer  142  includes a first proximal end and a first distal end and the third transformer (T 3 )  144  includes a second proximal end and a second distal end. The first and second outputs  302 A,  302 B of the second transformer  142  are located at the first proximal end and the first center tap  208 A is located at the first distal end. The third and fourth outputs  304 A,  304 B of the third transformer  144  are located at the second proximal end and the second center tap  208 B is located at the second distal end. The first proximal end of the second transformer  142  has a first distance from the second proximal end of the third transformer  144  and the first distal end of the second transformer  142  has a second distance from the second distal end of the third transformer  144 . In this example, the first distance is less than the second distance. In this manner, a distance of the first and second outputs  302 A,  302 B from the third and fourth outputs  304 A,  304 B is less than a distance of the first center tap  208 A from the second center tap  208 B. Accordingly, the first and second outputs  302 A,  302 B of the T 2  secondary winding  148  are close in physical distance to the third and fourth outputs  304 A,  304 B. 
     In the illustrated example of  FIG. 3 , the second transformer  142  includes first and second vertices  305 A,  305 B and the third transformer  144  includes third and fourth vertices  307 A,  307 B. The first vertex  305 A is located at the first proximal end (such as at the first and second outputs  302 A,  302 B) and the second vertex  305 B is located at the first distal end (such as the first center tap  208 A). The third vertex  307 A is located at the second proximal end (such as at the third and fourth outputs  304 A,  304 B) and the fourth vertex  307 B is located at the second distal end (such as at the second center tap  208 B). 
     In the illustrated example of  FIG. 3 , a first centerline  309 A is defined by the first vertex  305 A and the second vertex  305 B. A second centerline  309 B is defined by the third vertex  307 A and the fourth vertex  307 B. In  FIG. 3 , the first centerline  309 A and the central axis  301 A form the first angle  303 A and the second centerline  309 B and the central axis  301  form the second angle  303 B. In some examples, first centerline  309 A and the central axis  301  form an acute angle. In some examples, the second centerline  309 B and the central axis  301  form an acute angle. Additionally and/or alternatively, the first centerline  309 A and the central axis  301  may form any angle and the second centerline  309 B and the central axis  301  may form any angle. In some examples, the first centerline  309 A and the second centerline  309 B form a right angle. Additionally and/or alternatively, the first centerline  309 A and the second centerline  309 B for any angle. 
     Advantageously, the angled orientation of the second transformer  142  and the third transformer  144  improve the efficiency of the split-combine transformer  102  due to minimized routings at the split-combine outputs  306 A,  306 B. The routings at the split-combine outputs  306 A,  306 B are minimized relative to outputs of conventional split-combine transformer windings that are parallel to the central axis  301 . For example, because the distance of the first proximal end to the second proximal end is less than the distance of the first distal end to the second distal end, the first and second outputs  302 A,  302 B are close in physical distance to the third and fourth outputs  304 A,  304 B. Therefore, less routing is needed to connect the first output  302 A to the third output  304 A and to connect the second output  302 B to the fourth output  304 B. Less routing in an integrated circuit improves efficiency of the integrated circuit because low output impedance is sensitive to parasitic capacitances. Long routings in an integrated circuit increase the amount of parasitic capacitance and/or resistance in that integrated circuit. Therefore, by positioning the outputs of the secondary windings (such as outputs  302 A,  302 B,  304 A,  304 B of secondary windings  148 ,  152 ) closer together, the routings are shortened and the parasitic capacitances and/or resistances are reduced. 
     For example, a conventional power combiner includes two transformers and both transformers may be 100 microns by 100 microns. Such conventional transformers are parallel to a central axis (such as central axis  301 ) extending between the transformers and bisecting the outputs of the transformers. In order to connect to the secondary winding outputs of those transformers, at least 50 microns of routing from one transformer output and 50 microns of routing from the second transformer output are required to bring the first and second transformer outputs to a common point. However, angling the transformers (such as second transformer  142  and third transformer  144 ) relative to the central axis  301  enables the output of the transformers  142 ,  144  to be closer together near the common point and, thus, reduces the length of routing by 50% to 60% relative to conventional power combiners. Reducing the length of routing advantageously reduces the parasitic inductance of the secondary windings  148 ,  152 . If the parasitic inductance is smaller, the secondary windings  148 ,  152  can be bigger and still achieve the necessary inductance at the secondary side for matching purposes. Advantageously, the bigger the winding, the higher the coupling coefficient and quality factor. Therefore, minimizing the routing facilitates reducing parasitic inductance and increasing the coupling coefficient and quality factor. 
     Advantageously, the center taps  208 A,  208 B, and  210  are easily accessible, and thus enables quality design of a harmonically tuned and high efficiency power amplifier  100 . For example, the center taps  208 A,  208 B are located at respective first and second distal ends, which are located at respective distances from the central axis  301  that are greater than respective distances of the first and second proximal ends from the central axis  301 . In this manner, the center taps  208 A,  208 B are distanced from inputs  101 A,  101 B of the primary windings  146 ,  150  and from the outputs of the secondary windings  148 ,  152 , leaving them in an easily accessible position. By exposing the center taps  208 A,  208 B, a harmonic balancing network can be implemented at the secondary center taps (such as center taps  208 A,  208 B) to enforce a symmetric circuit operation, resulting in improved efficiency in the driver stage  104 . In this example, the primary center tap  210  is located between the primary windings  146 ,  150  and between only a portion of the secondary windings  148 ,  152 . For example, the primary center tap  210  is located near a corner and/or shorter edge of respective secondary windings  148 ,  152 . In a conventional split-combine transformer, the primary center tap may be located near the secondary winding outputs and/or near the longer edges of the secondary windings. Therefore, the location of the primary center tap  210  in the example split-combine transformer  102  avoids overlap and/or coupling between the center tap  210  and the secondary windings  148 ,  152 . Exposing the primary center tap  210  at the input of the split-combine transformer  102  facilitates harmonic termination which improves an output of the driver stage  104  and, thus, efficiency of the driver stage  104  and overall power of the power amplifier (such as power amplifier  100 ). 
       FIG. 4  is an example third schematic diagram  400  of the split-combine transformer  102  of  FIGS. 1 and 2 . The third schematic diagram  400  illustrates one layer (such as one metallization layer) of the split-combine transformer  102 . The layer corresponds to the material implementing the supply voltage decaps  202 ,the bias circuitry inputs  204 A,  204 B and ground routing. The layer is positioned under the first and second layers of the second and third transformers  142 ,  144 . For example, the material implementing the supply voltage decoupling capacitors  202  and the bias circuitry inputs  204 A,  204 B is positioned underneath the material implementing the primary windings  146 ,  150  and the secondary windings  148 ,  152 . 
       FIG. 5  is a graph  500  of output power of the example power amplifier  100  of  FIG. 1  with respect to operating frequency (fin) of the example power amplifier  100  of  FIGS. 1 . The graph  500  includes a first line  502 , a second line  504 , a third line  506 , and a fourth line  508 . The output power of the example power amplifier  100  is measured in terms of decibels per milliwatt (dBm) and the operating frequency of the power amplifier  100  is measured in terms of Giga hertz (GHz). 
     In  FIG. 5 , the first line  502 , the second line  504 , the third line  506 , and the fourth line  508  are indicative of a performance of the power amplifier  100  of  FIGS. 1 and 2 . For example, the first line  502  represents the output power of the power amplifier  100 , the second line  504  represents the collector efficiency, the third line  506  represents the power added efficiency of the power amplifier  100 , and the fourth line  508  represents the gain of the power amplifier  100 . 
     In  FIG. 5 , the PAE, represented by the third line  506 , is defined by a difference in output power to input power divided by DC power dissipation of the power amplifier  100 . The collector efficiency, represented by the second line  504 , is defined by output power of the power amplifier  100  divided by DC power dissipation of the power amplifier  100 . The gain, represented by the fourth line  508 , is defined by a ratio of output power to input power. 
     In this example, the power amplifier operating frequency is 76 GHz. The PAE is 25.8% when the power amplifier  100  is operating at 76 GHz. The output power of the power amplifier  100  is 17.5 dBm at the operating frequency. The gain of the power amplifier  100  at the operating frequency is 11.6 dBm. The collector efficiency of the power amplifier  100  is 27.7% at 76 GHz. These values of performance are an improvement relative to a conventional power amplifier without a 45 degree split-combine transformer. For example, an inter-stage matching network having one or more transformers with a 2:1 turn ratio and a small secondary coil degrades the quality factor by 10% to 15% and the coupling coefficient by at least 25%. In such an inter-stage matching network, the degradation of quality factor and coupling coefficient incurs higher interstage losses and eventually, the PAE degrades by about 10%. 
     In this description, the term “and/or” (when used in a form such as A, B and/or C) refers to any combination or subset of A, B, C, such as: (a) A alone; (b) B alone; (c) C alone; (d) A with B; (e) A with C; (f) B with C; and (g) A with B and with C. Also, as used herein, the phrase “at least one of A or B” (or “at least one of A and B”) refers to implementations including any of: (a) at least one A; (b) at least one B; and (c) at least one A and at least one B. 
     Example methods, apparatus and articles of manufacture described herein improve output power and efficiency of power amplifiers by implementing an inter-stage matching network between the driver stage and output stage that comprises two 1:1 transformers having a primary windings connected in series and secondary windings connected in parallel. Efficiency is improved in the power amplifier by using a 1:1 turn ratio to increase the coupling coefficient of the transformers. Efficiency is improved in the power amplifier by angling the transformers in a 45 degree angle relative to a centerline, where the outputs of the secondary windings are closest to the centerline to reduce parasitic routing in the power amplifier and, thus, increasing the quality factor of the transformers. The angling of the transformers enables an accessibility to the center taps that is not easily accessible in conventional power amplifiers. Such accessibility enables and/or facilitates harmonically tuning power amplifiers to increase efficiency of the power amplifier. The output power of the power amplifier is increased due to the parallel couplings of the secondary windings of the transformers. 
     Modifications are possible in the described embodiments, and other embodiments are possible, within the scope of the claims.