Patent Publication Number: US-7917117-B2

Title: Auto-tuning amplifier

Description:
TECHNICAL FIELD 
     This document pertains generally to amplifiers, and more particularly, but not by way of limitation, to an auto-tuning amplifier. 
     BACKGROUND 
     Portable transceiver devices, such as those found in mobile telephones, typically require coverage for a number of narrow frequency bands. Historically, circuits designed for such low power transceivers have relied on a number of individual front ends with each tuned to a particular frequency band. This approach, however, has drawbacks. Each front end uses an on-chip inductor which occupies a relatively large portion of the available die space. Also, variations in the fabrication process, operating voltage, and operating temperatures, can lead to reduced yield and costly calibration requirements. For these and other reasons, the front end circuits currently used in portable transceivers are inadequate. 
     OVERVIEW 
     An example of the present subject matter can be configured to tune a frequency of a resonant circuit using a control loop based on a phase shift through the resonant circuit. The resonant circuit can include, in various examples, a filter, an amplifier, or other module and in this document, the resonant circuit is referred to as a gain stage. 
     By way of example, a center frequency of a low noise amplifier can be controlled by one or more tunable tank circuits. The tank circuit can include tunable inductors and switched capacitors. The amplifier can be used, for example, in a front end of a radio frequency (RF) transceiver such as that found in a cellular telephone. 
     A resonant frequency of a tank circuit can be selected using a signal proportional to a phase difference between an amplifier stage output signal and a reference signal. A center frequency of the low noise amplifier is determined by the resonant frequency of the tank circuit. 
     One example of the present subject matter provides good immunity to variations in process, voltage, and temperature (PVT). In addition, a wide tuning range is provided without the burden of providing individual front ends for each frequency band. 
     An example circuit as described herein can be configured as an RF receiver with a frequency that can be locked to a center frequency based on a reference frequency. The circuit can be configured as a single frequency band low noise amplifier or as a multi-band low noise amplifier. In addition, an example circuit can be configured to have an input or output impedance which can be matched to another circuit at one or multiple selected frequencies. 
     This overview is intended to provide an overview of subject matter of the present patent application. It is not intended to provide an exclusive or exhaustive explanation of the invention. The detailed description is included to provide further information about the present patent application. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the drawings, which are not necessarily drawn to scale, like numerals may describe similar components in different views. Like numerals having different letter suffixes may represent different instances of similar components. The drawings illustrate generally, by way of example, but not by way of limitation, various embodiments discussed in the present document. 
         FIG. 1  illustrates a block diagram of an amplifier. 
         FIG. 2  illustrates a schematic of a multi-stage amplifier. 
         FIGS. 3A and 3B  illustrate schematics of tank controllers. 
         FIG. 4  illustrates a schematic of a reference signal source. 
         FIG. 5  illustrates a schematic of a tank circuit. 
         FIG. 6  illustrates a phase diagram for an amplifier. 
         FIG. 7  illustrates a schematic of an amplifier using field effect transistors. 
         FIG. 8  illustrates a schematic of a hybrid CG/CS amplifier. 
         FIG. 9  illustrates a method according to an example of the present subject matter. 
         FIGS. 10A ,  10 B, and  10 C illustrate a schematic of an amplifier. 
         FIGS. 11A and 11B  illustrate a schematic of an amplifier. 
         FIG. 12  illustrates a block diagram of a circuit. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  illustrates a block diagram of amplifier  100 A according to one example. In the figure, gain stage  120 A receives an input at node  84  and provides an output at node  88 . Gain stage  120 A is coupled to a resonant circuit, herein referred to as tank circuit  160 A. The output at node  88  is coupled to a tank control circuit, herein referred to as tank controller  140 A. In addition, reference signal source  150 A provides an output to tank controller  140 A (at node  82 ) and an output at node  84 . An output of tank controller  140 A is coupled, at node  86 , to control input of tank circuit  160 A. 
     Tank circuit  160 A can be used for impedance matching of inputs or impedance matching of a load section of an amplifier, and in this example, is shown coupled to the gain stage. Tank circuit  160 A can be coupled to a gain stage in various manners, including, for example, at the input to the gain stage, at the output of the gain stage, or at an intermediary location in the gain stage. In various examples, the tank circuit can be coupled in a drain circuit, a source circuit, or a gate circuit of a field effect transistor (FET). A resonant frequency of the tank circuit determines the center frequency of the gain stage. One end of the tank circuit is coupled to a ground potential or other reference level. 
     Reference signal source  150 A provides two outputs, one of which is provided to the input of gain stage  120 A and the other of which is provided to tank controller  140 A. A phase difference between the reference signal, as seen at node  82 , and the amplified signal, as seen at node  88 , is used by tank controller  140 A to generate a correction signal on node  86 . The correction signal at node  86  is used to adjust a resonant frequency of tank circuit  160 A. A center frequency of gain stage  120 A is determined by the resonant frequency of tank circuit  160 A. 
     Reference signal source  150 A, in various examples, provides a current output reference and a voltage output, two current outputs, or two voltage outputs. In one example, the signal at node  82  is a voltage and the signal at node  84  is a current. The two outputs from reference signal source  150 A can differ in phase from −180 degrees to +180 degrees. 
     Gain stage  120 A can include a low noise amplifier or a portion of a filter and can have either single or differential inputs and outputs. Gain stage  120 A can include multiple sections or a single section. In one example, gain stage  120 A includes an RF amplifier. 
     Consider the operation of circuit  100 A schematically illustrated in  FIG. 1 . In the example shown, reference signal source  150 A provides a reference signal that is applied to an input of gain stage  120 A. Using tank controller  140 A, a signal at the output of gain stage  120 A is compared with a signal provided by reference signal source  150 A. Tank controller  140 A, in the example illustrated, provides a DC output signal that is related to a phase difference between the gain stage output and the reference signal source. 
     The present subject can be configured to operate in a homodyne mode (in which the phase comparison is done at the center frequency of the amplifier or a sub-harmonic of that frequency) or in a heterodyne mode (in which the reference signal and output are shifted to a more convenient frequency to make the phase comparison). 
     The DC phase detector output signal can be described as an error signal. The tank controller provides an output, at node  86 , that adjusts the resonant frequency of tank circuit  160 A. The resonant frequency of tank circuit  160 A is adjusted in a manner to bring the amplifier center frequency closer to the frequency of the reference signal (along with any offset). 
       FIG. 2  illustrates a schematic of a multi-stage amplifier  100 B having input  112  and output  130 . Amplifier  100 B includes gain stage  120 B and gain stage  120 C coupled in series. Tank circuit  160 B, at input to gain stage  120 B, tank circuit  160 C at input to gain stage  120 C, and tank circuit  160 D at output of gain stage  120 C are identical matching circuits (replicas) each having a variable resonant frequency. 
     Reference signal source  150 B provides a reference signal to node  84  at the input of gain stage  120 C and also provides a reference signal to node  82  at the input of tank controller  140 B. Tank controller  140 B also receives an input from node  88  at the output of gain stage  120 C. 
     Tank controller  140 B provides an output at node  86  coupled to tank circuit  160 B, tank circuit  160 C, and tank circuit  160 D. The control signal on node  86  is sometimes referred to as S CTR  and can include any combination of an analog signal, a digital signal, or a combination of analog and digital signals. 
       FIG. 3A  illustrates an example of tank controller  140 C. Tank controller  140 C includes phase detector  32 A and filter  34 A. Phase detector  32 A is configured for homodyne operation. 
     Phase detector  32 A receives an input from node  88  (output of a gain stage) and node  82  (output of a reference signal source, such as a local oscillator). In one example, phase detector  32 A provides an output signal, on node  36 , that is proportional to a difference in phase as to a signal on node  82  and a signal on node  88 . The phase relationship between the reference signal and the gain stage can be determined using a mixer or a phase detector. Phase detector  32 A can include a frequency mixer or analog multiplier circuit. Detector  32 A generates a current or voltage signal which represents the difference in phase between two signal inputs. 
     In other examples, the phase detector provides an output signal, on node  36 , that bears some relationship to a difference in phase as to the signal on node  82  and the signal on node  88 . For instance, the relationship can be linearly related or non-linearly related. 
     Filter  34 A generates an output at node  86  based on the input signal on node  36 . In one example, filter  34 A, also referred to as a loop filter, serves to filter the output from phase detector  32 A and create a stable lock that converges at the correct frequency. In one example, filter  34 A includes a differential amplifier and an integrator. 
     The control signal provided by the tank controller and to the tank circuit can take a variety of forms. For example, the control signal can include a modulated analog signal on a line, an encoded digital signal, a bus having a number of digital lines, or a combination of digital and analog signals. In one example, the tank controller includes circuitry to implement a digital controller and is configured to generate a digital control signal. 
       FIG. 3B  illustrates an example of tank controller  140 D configured for heterodyne operation. Tank controller  140 D includes multiplier  32 B, multiplier  32 C, and phase detector  33  arranged to operate in a heterodyne configuration. As noted earlier, a phase detector can include a frequency mixer or analog multiplier circuit. Multiplier  32 B receives a first local oscillator signal on node  82  and a second local oscillator signal on node  83 . In the example illustrated, the output of multiplier  32 B is a voltage that represents the intermediate frequency which is provided to an input of phase detector  33 . In addition, multiplier  32 C receives a signal on node  88  (which corresponds to the amplifier output), and a phase shifted (through phase shifter  46 A) signal from the second local oscillator signal, also denoted as node  83 . The output of multiplier  32 C is provided to an input of phase detector  33 . The output of phase detector appears at node  36  which is provided to loop filter  34 . Multiplier  32 B and multiplier  32 C allow the frequency to be raised or lowered. 
     In  FIG. 3B , phase shifter  46 A is shown beyond the boundaries of the dashed line. The dashed lines of this and the other figures, however, are for organizational purposes only and are not to be construed as limiting the location of any particular component. Note, for example, that phase shifter  46 B, of  FIG. 4 , can also be viewed as part of reference signal source  150 C. 
       FIG. 4  illustrates reference signal source  150 C having an output at both node  84  and at node  82 . Oscillator  44  provides a stable reference signal having a single frequency. In various examples, oscillator  44  includes a local oscillator, a synthesizer, or other circuit configured to provide a reference frequency. 
     In the figure, oscillator  44  has one output coupled to buffer  42  and another output coupled to phase shifter  46 B. Buffer  42  provides isolation, and in various examples, provides attenuation (negative gain) or amplification (positive gain). An output from buffer  42  is provided at node  84 . Phase shifter  46 B provides a phase shifted version of oscillator  44  output at node  82 . In one example, phase shifter  46 B provides 90 degrees of phase shift. Phase shifter  46 B can be configured to provide other amounts of shift, including, for example, 45 degrees. An amount of shift can be selected for the phase shifter to cause the frequency to lock on a particular target frequency or displaced to one side by a selected amount. 
       FIG. 5  illustrates tank circuit  160 E. In the figure, tank circuit  160 E includes a resonant circuit and is depicted as a parallel connection of capacitor  52 , resistor  54 , and inductor  56 . The components shown in the schematic can represent actual or parasitic components. Tank circuit  160 E resonates at a frequency determined by the capacitance value and the inductance value of the components. At a resonant frequency, the tank circuit appears as a pure resistance having no reactive component. 
     At least one component of tank circuit  160 E is adjustable and thus, the resonant frequency is adjustable. In the figure, inductor  56  is denoted as having a variable inductance, however capacitor  52  can also be made variable. A signal on node  86  determines the resonant frequency of tank circuit  160 E. In the figure, tank circuit  160 E is coupled to node  84  and also coupled to a reference potential, which, in various examples, includes a ground or other reference voltage. 
     In the figure, tank circuit  160 E includes passive electrical components, however, one or more of the components shown can be replaced with an active component or active circuit that is fabricated, for example, using a semiconductor manufacturing process. For example, tank circuit  160 E can include a varactor, a variable capacitor (such as a switched capacitor or a tunable capacitor), or a variable inductor (such as a switched inductor or a tunable inductor). The variable inductor can include, for example, a capacitor or inductor tuned through an active variable gain element. A capacitor can be tuned through the Miller Effect by varying the gain of a parallel voltage amplifier. Likewise, an inductor can be tuned by varying the current gain through two windings of a tightly coupled transformer. The tank circuit can include one or more components fabricated using a metal-oxide-semiconductor (also known as MOS), bipolar MOS (also known as BiCMOS), silicon-germanium (SiGe), gallium arsenide (GaAs), or any of a number of other fabrication technologies. For example, a tank circuit can be included on a monolithic microwave integrated circuit (MMIC). In one example, the tank circuit includes a transmission line. 
     In one example, a number of tank circuits are fabricated on a single semiconductor chip and are said to be replicas of each other. The fabrication process assures that each tank circuit will, to a high degree, be identical replicas of each other tank circuit. Note, however, that the different tank circuits can be coupled to different reference voltages (such as gnd and vdd). In addition, different tank circuits can have resistors that differ without altering the center frequency. 
     An example of the present subject matter includes a low noise amplifier that can be tuned across a wide band of frequencies. The center frequency of the amplifier can be accurately tuned based on a frequency provided by a local oscillator or by a synthesizer. 
     One example of the present subject matter operates in manner that can be described as a master-slave relationship. The one or more tank circuits are adjusted as a unit in accordance with a detected phase difference between the output of the amplifier and the reference signal source. The reference signal source provides a calibration reference to the master circuit. The slave circuit is adjusted with the same control signal as the master although it does not see the reference signal. In one example, one tank circuit of the amplifier is a replica of another tank circuit and the center frequency of the amplifier can be adjusted by changing the resonant frequency of the tank circuits. 
     The present subject matter is largely immune to variations in manufacturing process, operating voltage and temperature variations. One example allows an amplifier to lock onto a particular phase difference and provide a tuned amplifier suitable for use as a low noise front end for a receiver. 
     Some of the components used in the present subject matter can fulfill a dual role. In particular, some components (or modules) of the present subject matter can be used for other components in a typical receiver. For example, an output from the local oscillator in an RF receiver can be used as the reference signal source. For example, a mixer used in a receiver front end can also be used as a detector and the reference signal can be drawn from a local oscillator (LO). In some receivers, a mixer is driven by an in-phase (I) local oscillator signal and a quadrature (Q) local oscillator signal that is displaced by a 90 degree phase shift relative to the I signal. The phase shift can be provided by a quadrature LO signal such as that provided by a quadrature voltage controlled oscillator (QVCO) or a polyphase filter. 
     In one example, a constant offset is used between the resonant frequency and the reference signal frequency. The offset can be selected to cancel out the effects caused by the parasitic phase through the circuit (assuming the phase comparator is an analog multiplier). For example, with a 0.4 GHz offset, the reference frequency is set at 2.5 GHz to provide a target amplifier center frequency of 2.1 GHz. Assuming the phase detector is an analog multiplier, and the remainder of the circuit introduces no phase lag and the 90 degree phase shifted signal is used as the reference in the multiplier, then the tank circuit is set to resonate at the target frequency. 
     In various examples, phase detector  32 A (or phase detector  32 D) includes a mixer, a multiplier, or other type of detector that generates a signal representative of a difference in phase between the two signal inputs. 
       FIG. 6  graphically illustrates phase as a function of frequency normalized to bandwidth for a low noise amplifier. As noted in the graph, phase differences are linear in the region near the resonant frequency, and at resonance, the phase shift is zero. The figure illustrates performance using a two-stage amplifier. The slope of the graph at resonance becomes steeper with increasing number of gain stages. 
     The derivative of the phase with respect to frequency can be expressed as: 
     
       
         
           
             
               
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                       1 
                     
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                       Q 
                       2 
                     
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                       Q 
                       3 
                     
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                     … 
                   
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     A signal proportional to phase is used as a loop error signal for a phase locked loop (PLL) and can be used to lock the amplifier center frequency onto resonance. 
     The amount of offset is a function of the number of stages and is proportional to the inverse of Q. The reference frequency and the particular resonant frequency of the tank circuit is substantially matched when it is within a few 3 dB bandwidths of the resonant structure. In one example, the amplifier center frequency is tuned to a frequency having a power within 5 dB of the resonant frequency of the tank circuit. 
     A transfer function can be used to describe the relation between the input and output of the gain stage. In particular, the center frequency of the gain stage can be inferred from the transfer function. In various examples of the present subject matter, the tank circuit of the gain stage is adjusted based on a detected phase and the amount of injected signal (or tank controller gain) is adjusted according to the detected amplitude. 
     In one example, an amplitude of the amplifier transfer function is detected and used to provide a control signal. Near the center frequency, the amplitude exhibits a quadratic relationship. A derivative of the amplitude function can be used to provide a control signal, however, this may produce a loop error. The derivative information is a derived quantity which can lead to a dead band which may frustrate the frequency lock. In addition, the amplitude detection may be prone to stability problems because it is sensitive to the gain setting of the amplifier. 
     Other portions of this document describe examples in which the phase of the amplifier is used to generate the control signal for the tank circuit. 
     In one example, both the phase and amplitude of the transfer function are detected and used to provide a control signal to the tank circuit. The phase difference may be suited for making changes in the resonant frequency of the tank circuit and the amplitude of the signal can be used for control of the control loop gain. 
     The present subject matter can be implemented using gain stages provided by field effect transistors.  FIG. 7  illustrates a schematic of amplifier  700  using field effect transistors. In the figure, a reference signal frequency is provided by a local oscillator here denoted as source  705 , which is injected at two locations in the circuit. Tank circuit  710 , tank circuit  720 , tank circuit  730 , and tank circuit  740  are replica circuits, with each having an adjustable capacitance. Transistors provide the three gain stages in this circuit and are denoted as transistor  760 , transistor  770 , and transistor  780 . 
     The reference signal from source  705  is injected at transistor  750  and at the detector  792  of the tank controller  790 . Transistor  760  receives a bias voltage and the amplifier input signal. Capacitor  768  and capacitor  778  provide inter-stage coupling. Transistor  780  provides an amplifier output signal and also provides a signal to detector  792 . Tank controller  790  also includes loop filter  794  which provides the correction signal denoted as S CTR    796 . Control signal S CTR    796  can include a voltage (direct current or alternating current), a current (DC or AC), a digital signal or a combination of a digital and analog signal configured to adjust the resonant frequency of tank circuit  710 , tank circuit  720 , tank circuit  730 , and tank circuit  740 . The controllable elements of the tank circuits are denoted with a diagonal line and the connection between S CTR  and the tank circuits are omitted in the figure for purposes of clarity. 
     Circuit  700 , as illustrated in the figure, includes a matched 50 ohm input/output RF tunable amplifier having low noise and a wide tuning range. 
     Other applications (in addition to RF circuits) are also contemplated. For example, the circuit can be configured for operation using a microwave signal. In such a circuit, the tuning of the tank circuit is controlled for use with an input signal in the microwave spectrum. 
       FIG. 8  illustrates circuit  800  for a hybrid common gate/common source (CG/CS) amplifier having differential input and differential output. In circuit  800 , CG amplifier (provided by transistor  810  and transistor  820 ) receives the input signal positive (at  806 ) and signal negative (at  808 ). In addition, CS amplifier, as provided by transistor  830  and transistor  840 , also are coupled to signal positive  806  and signal negative  808 , respectively. The drain of transistor  810  and drain of transistor  840  are coupled to load positive  802  and the drain of transistor  820  and drain of transistor  830  are coupled to load negative  804 . The gates of transistor  830  and transistor  840  connect to coupling capacitor  828  and coupling capacitor  838 , respectively. DC biasing circuitry can take various forms and is not treated exhaustively in this document. Tank circuit  850  and tank circuit  860  include an adjustable element used to tune a resonant frequency. In the figure, the adjustable element includes a capacitor, however, other reactive components (passive or active) can also be adjusted to tune the resonant frequency. Tank circuit  850  and tank circuit  860  are both coupled to a tank controller not shown in the figure. 
     A single-ended-to-differential amplifier can include inputs of the CG amplifier and inputs of CS amplifiers connected together and drains/collectors of the transconductors attached to separate loads or to a differential load. A standard differential pair can serve as an additional gain stage. 
     The circuits illustrated herein can be fabricated using other technology. For example, when using bipolar junction (BJT) devices, the gates are replaced by bases and the sources are replaced by emitters and the drains are replaced by collectors. When using BiCMOS, either or both transconductors can be BJT devices. In one example, cascode devices are used. 
     The reference signal can be injected into the multiple gain stages at any of a plurality of sites. For example, the reference signal can be injected at an input to a first stage or a later stage. In addition, the amplifier transfer function can be examined by monitoring an output signal at some location downstream of the injection site. The site of the output signal can be selected as the last stage in a multi-stage amplifier or any prior stage in the amplifier that is downstream of the reference signal injection site. 
     Other options for injecting the reference signal also exist. For example, a test signal can be simultaneously injected into multiple gain stages for a flatter gain response far off resonance. As another example, the test signal can be sequentially injected into different gain stages to tune an amplifier. In one particular example, the test signal is injected into a last gain stage in a series, then that stage is tuned, and in turn, successively earlier gain stages receive the injected signal and are tuned until the whole amplifier is tuned. 
     If a fixed offset is used, then simulation of the chosen topology can provide a first order correction to the frequency between the reference frequency at lock and the resonant frequency of the replica tank circuit. If a quadrature signal is used, then the reference signal source can be tuned directly to the center of the tank circuit. In one example, a phase offset of 90 degrees (plus or minus) is selected, in this case, if there are no other phase shifts, the signal source or tank controller can omit the phase shifter. 
       FIG. 9  illustrates method  900  for operating an example of the present subject matter. At  910 , an output signal is generated using the gain stage, amplifier, or other circuit. As a function of the circuit configuration and components, including such variables as process, voltage and temperature, the circuit will exhibit a particular center frequency. The center frequency of the circuit is adjustable based on the resonance frequency of the tank circuit. As noted, the tank circuit can be at an input, an output or at an intermediary portion of the circuit. 
     At  920 , a control signal is generated. The control signal, in one example, uses the output signal and a reference signal source. For instance, a phase difference between a frequency of the output signal and a frequency of the reference signal can be used to generate a control signal. The control signal, in one example, is a direct current signal having a voltage (or current) level related to the phase difference. The control signal, sometimes referred to as S CTR , can include an analog signal encoded as a voltage (AC or DC), an analog signal encoded as a current (AC or DC), a digital signal (encoded on a bus or on a digital signal single line), or a combination of analog or digital signals. 
     At  930 , the control signal is used to determine a resonant frequency of at least one tank circuit. At least one tank circuit includes a reactance having a value that is selectable based on the control signal in the absence of other parasitics. The reactance can include a variable capacitor, a variable inductor, or both a variable capacitor and a variable inductor. The resonance frequency of the tank circuit is proportional to the reciprocal of the square root of the capacitance. 
     At  940 , the tank circuit is adjusted to shift the resonant frequency in a manner that reduces the phase difference between the output signal and the reference signal. The injected signal is variously referred to as a test signal or a reference signal. The tank circuit is adjusted by changing a value of a capacitance, by changing a value of an inductance, or by changing a value of both a capacitance and an inductance. 
     The present subject matter can be configured as a cross-coupled common gate front end. 
       FIG. 10A ,  FIG. 10B , and  FIG. 10C  illustrate portions of an amplifier according to the present subject matter.  FIG. 10A  illustrates circuit  1000  having tunable tank circuit  1050  and tunable tank circuit  1060 . In the figure, tank circuit  1050  and tank circuit  1060  include a fixed inductor and an adjustable capacitor. The capacitance of the adjustable capacitors, and thus the resonant frequency of the tank circuits, are determined by a control signal, here denoted as V T . Tank circuit  1050  receives current I ref  and is coupled to V A,P  (positive) and V A,M  (minus or negative). Tank circuit  1060  is coupled to V IN,P  (positive) and V IN,M  (minus or negative). Transistor  1010  and transistor  1030  are connected in series between V A,P  and V IN,P . Transistor  1020  and transistor  1040  are connected in series between V A,M  and V IN,M . The gate of transistor  1010  and the gate of transistor  1020  are connected to a common reference and the gate of transistor  1030  and the gate of transistor  1040  are also connected to a common reference. 
     In  FIG. 10B , control signal V T  of circuit  1100  is provided by tank controller  1110 . Tank controller  1110  receives a differential signal from differential detector  1115 . the differential signal received by tank controller  1110  is proportional to differential signal V ref,Q  and a differential signal provided by series transistors  1120  and series transistors  1125 . In the figure, series transistors  1120  and series transistors  1125  are cascode pairs, and receive V A,M  and V A,P , respectively. 
       FIG. 10C  illustrates circuit  1150  configured to provide current I ref . In the figure, circuit  1155  receives a differential signal which may be in quadrature (V I  and V Q  are 90 degrees, or a quarter period apart with the I-phase signal V I  either leading or lagging the Q-phase signal V Q ). Phase offset is provided by phase shifter  1160  and an output voltage is translated to a current by circuit  1165 . 
       FIG. 11A  illustrates circuit  1200  having cascode transistors  1220  and transistors  1225  which are coupled to differential detector  1215 . Detector  1215  also receives differential V ref,I  and provides a differential signal to gain controller  1210 . Gain controller  1210  provides automatic gain control voltage V AGC , which in various examples can be an analog voltage, a digital voltage, or other type of control signal as described elsewhere in this document with respect to S CTR . 
     Circuit  1250  of  FIG. 11B  corresponds to circuit  1150  of  FIG. 10C  with the addition of input V AGC  to voltage to current converter circuit  1265  as shown. In particular, circuit  1255  generates a differential signal which may be in quadrature (V I  and V Q  are 90 degrees, or a quarter period apart with the I-phase signal V I  either leading or lagging the Q-phase signal V Q ). Phase offset is provided by phase shifter  1260  and an output voltage is translated to a current by circuit  1265 . 
     The circuits of  FIG. 10  and  FIG. 11  are examples of pseudo-differential amplifiers having greater headroom than that of a differential circuit with a tail current source. The circuits can be adapted for full differential operation as well. 
     Some phase is lost in the cascode node. This can be modeled by a simulator and inaccuracy arising from PVT will be of a second order. These losses can be compensated for by adjusting the phase shifter, by selecting V ref  at a frequency offset from the target circuit center frequency, or by adjusting both the phase shifter and V ref . 
     In at least one example, a compensation capacitor is used. The compensation capacitors are used in a master-slave architecture and are selected based on parasitic factors and inaccuracies due to drain/source/gate asymmetries. A value for the compensation capacitor can be found experimentally, by simulation, or by other methods. 
       FIG. 12  illustrates a block diagram of circuit  100 C. In the figure, the reference signal, provided by source  1280 , is injected as a square wave current at the N th  sub-harmonic of the target amplifier frequency, that is f(0)/N. The harmonic content of the injected signal excites tank circuit  160 F at the frequency f(0) through cascode transistors  1285 . The output of the amplifier (as seen through gain stage  120 D and gain stage  120 E) is put through divide-by-N circuit  1270 , after which the phase is compared (at phase detector  32 D) with a phase shifted (by phase shifter  1275 ) reference signal. The output of phase detector  32 D is sent to loop filter  34 B which outputs a control signal (S CTR ) for tank circuit  160 F. Circuit  100 C uses no local oscillator and no mixing to DC is needed in the control loop. 
     Circuit  100 C uses a phase difference to tune the circuit but rather than comparing at the same frequency, this circuit illustrates injecting a signal with phase coherent harmonic content. The divider circuit (divide-by-N circuit  1270 ) brings the amplifier output back down to the fundamental of the injected signal. Phase detection is then conducted at a lower frequency which, in some circuits, requires less power. In addition, for some applications, it is convenient to generate and provide a square wave (such as the output of a dual modulus divider in a fractional synthesis system, possibly with noise shaping). 
     ADDITIONAL EXAMPLES 
     A circuit as described herein, when configured as a tunable narrowband amplifier, provides satisfactory performance at a low power along with relaxed requirements for linearity and a lower noise. In addition, the wide tuning range of the present subject provides the flexibility of a wideband amplifier. 
     In one example, an amplitude of the signal through the amplifier is modulated to adjust the gain of the loop. In one example, the in-phase signal is mixed with the RF signal to generate a reference amplitude from the two signals and the reference amplitude is used to modulate the gain for the control loop. 
     The tuning loop of the present subject matter, including the tank controller and the adjustable tank circuits, can be operated continuously or on an as-needed basis. Continuous operation of the tuning loop can be used in applications having a frequency of the reference signal source that is offset from the target band. The tuning loop can be operated on an as-needed basis when, for example, a temperature change is detected, a voltage change is detected, or when a frequency band is changed. 
     When operating at a frequency that is significantly different than the resonant frequency of the one or more tank circuits, the loop gain may be too low. In one example, the reference signal source includes a PLL used to control the frequency of the reference signal source and the tuning loop time constant can be selected to be faster than that of a synthesizer of the PLL. The tuning loop characteristics are rather tolerant and need not converge too closely to the target value. 
     The present subject matter can be used with a low noise amplifier having a fixed or variable gain. 
     The reference signal can be provided by various circuits. In one example, a reference signal is provided by a circuit having a slew rate that is limited such that a gain of the controller remains above a selected level. 
     Additional Notes 
     The above detailed description includes references to the accompanying drawings, which form a part of the detailed description. The drawings show, by way of illustration, specific embodiments in which the invention can be practiced. These embodiments are also referred to herein as “examples.” Such examples can include elements in addition to those shown and described. However, the present inventors also contemplate examples in which only those elements shown and described are provided. 
     All publications, patents, and patent documents referred to in this document are incorporated by reference herein in their entirety, as though individually incorporated by reference. In the event of inconsistent usages between this document and those documents so incorporated by reference, the usage in the incorporated reference(s) should be considered supplementary to that of this document; for irreconcilable inconsistencies, the usage in this document controls. 
     In this document, the terms “a” or “an” are used, as is common in patent documents, to include one or more than one, independent of any other instances or usages of “at least one” or “one or more.” In this document, the term “or” is used to refer to a nonexclusive or, such that “A or B” includes “A but not B.” “B but not A,” and “A and B,” unless otherwise indicated. In the appended claims, the terms “including” and “in which” are used as the plain-English equivalents of the respective terms “comprising” and “wherein.” Also, in the following claims, the terms “including” and “comprising” are open-ended, that is, a system, device, article, or process that includes elements in addition to those listed after such a term in a claim are still deemed to fall within the scope of that claim. Moreover, in the following claims, the terms “first,” “second,” and “third,” etc. are used merely as labels, and are not intended to impose numerical requirements on their objects. 
     The above description is intended to be illustrative, and not restrictive. For example, the above-described examples (or one or more aspects thereof) may be used in combination with each other. Other embodiments can be used, such as by one of ordinary skill in the art upon reviewing the above description. The Abstract is provided to comply with 37 C.F.R. §1.72(b), to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. Also, in the above Detailed Description, various features may be grouped together to streamline the disclosure. This should not be interpreted as intending that an unclaimed disclosed feature is essential to any claim. Rather, inventive subject matter may lie in less than all features of a particular disclosed embodiment. Thus, the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separate embodiment. The scope of the invention should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.