Abstract:
An amplifier circuit according to one embodiment of the present invention comprises an amplifier transistor configured to amplify an input signal received at a terminal of the amplifier transistor, and a bias circuit having a bias transistor forming a current mirror with the amplifier transistor for stabilizing a bias operating point for the amplifier transistor, a buffer transistor coupled to the bias transistor and to the amplifier transistor, and a current source coupled to the buffer transistor and configured to generate a temperature-dependent current for injection into the buffer transistor. The buffer transistor improves linearity of the amplifier transistor by creating a predistortion of the input signal, and the current source injects the temperature-dependent current into the buffer transistor to adjust the extent of predistortion and to compensate for undesirable effects caused by variations in ambient conditions.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]     The present application claims the benefit of and priority to U.S. Provisional patent application No. 60/575,573 entitled “Amplifier Linearity Enhancement with Temperature-Compensated Predistortion Bias Circuit,” filed on May 28, 2004, the entire disclosure of which is incorporated herein by reference. 
     
    
     FIELD OF THE INVENTION  
       [0002]     The present invention relates in general to amplifier linearity enhancement technologies, and more particularly to a linearity-enhanced amplifier with a temperature-compensated predistortion bias circuit to achieve temperature-independent linearity as well as temperature-stable amplification.  
       BACKGROUND OF THE INVENTION  
       [0003]     The performance of microwave amplifiers based on heterostructure bipolar transistors generally improves with increased collector current density up to certain optimal point determined by a number of complex effects. Due to reliability limitations, however, the collector current density at which a heterostructure bipolar transistor can be operated is often set at a value below the maximum achievable gain. In order to ensure consistent performance, it is also important that this current density be maintained during normal variations in operating conditions, and in particular over a range of ambient temperature at which the amplifier is expected to operate.  
         [0004]     It is well-known that the collector current in a forward active region of a bipolar transistor is exponentially related to the temperature approximately as follows: 
 
 I   C   =I   S e q     V     BE     /kT   ( V   BE   &gt;&gt;kT/q )   (1) 
 
 where I c  is the collector current, I S  is a constant, q is the electron charge, k is Boltzmann&#39;s constant, V BE  is the base to emitter voltage, and T is the temperature in Kelvin.  FIG. 1  illustrates a conventional amplifier circuit  100 , in which a conventional resistive voltage divider  110 , formed using resistors R b1  and R b2 , is used to set a DC bias at the base of bipolar transistor Q RF , the collector of which is biased through a serially connected inductor L 1  between a power supply V CC  and ground. It can be expected that, based on Eq. (1), the transistor collector current I c  would vary significantly as a function of temperature. 
 
         [0005]     Various solutions are known in the art to stabilize the operating current of a bipolar transistor. In an amplifier circuit  200  shown in  FIG. 2 , a bias resistor R b  is added to be in series with the voltage divider  110 . This improvement is simple and inexpensive, and introduces a negative DC feedback for improved bias stability over temperature. It has a disadvantage, however, because the bias resistor R b  dissipates significant DC power and reduces the voltage available for forming a collector bias thereby reducing power output capability of the amplifier circuit.  
         [0006]      FIG. 3  illustrates a conventional amplifier circuit  300 , which employs a current mirror arrangement to stabilize a bias operating point for the transistor Q RF  without the drawbacks of the series bias resistor approach in circuit  200 . As shown in  FIG. 3 , a bias transistor Q b1  is introduced, which is similar to transitor Q RF  but with a smaller periphery. A reference current I r  through the bias transistor is fixed by bias resistors R b1  and R b2 , and a controlled voltage at the base of transistor Q b1  provides a temperature-compensated bias voltage to the base of transistor Q RF  through a base resistor R b3 . In this fashion, the base-emitter voltage of Q RF  is controlled to maintain a constant collector current proportional to the reference current I r  through transistor Q b1 .  
         [0007]     The disadvantages of circuit  300  are two-fold. First, the resistance associated with base resistor R b3 , which is provided to minimize coupling of an RF input signal into the base of transistor Q b1 , needs to be large compared to an input impedance of transistor Q RF , which is typically around 50 ohms. Thus, R b3  is typically on the order of a few hundred ohms. Since the base current of transistor Q RF  may be significantly large, a significant voltage drop occurs across resistor R b3 , which decouples the base-emitter DC voltage of transistor Q RF  from that of transistor Q b1 . Secondly, because the relatively large base current of transistor Q RF  is drawn from the reference current I r  through R b1 , a significant mismatch between the reference current I r  through R b1  and the collector current of transistor Q b1  is thus introduced. As a result, the base current through R b3  and the collector current through Q b1  would vary significantly as the current gain value β of transistor Q RF  changes over temperature. This in turn would result in undesirable bias current variations in Q RF  over temperature.  
         [0008]      FIG. 4  illustrates a conventional amplifier circuit  400  employing an improved current mirror with a buffer transistor Q b2  as a current buffer. Transistor Q b2  provides a source for the base currents of transistors Q RF  and Q b1 , while its own base current, which comes through a resistor R b4 , can be small in comparison. Circuit  400  further includes a second base resistor R b5  serially coupled with base resistor R b3 . Base resistor R b5  can have a small resistance to avoid excessive DC voltage variations at the base of transistor Q RF , while base resistor R b3  can remain large to isolate transistor Q b1  from the RF input signal. As a consequence, however, the emitter-base junction of transistor Q b2  is inevitably exposed to a sizable fraction of the input RF signal. Therefore, as this junction is forward-biased in normal operation, it will have a highly nonlinear capacitance and current with respect to an input voltage, resulting effectively in a nonlinear load being presented to the RF input signal, in addition to that provided by the base-emitter junction of transistor Q RF . Thus, a predistortion of the input signal to transistor Q RF  can occur as a result.  
         [0009]     Linearity is important in many applications, and particularly in microwave communications, where distortion or departure from linearity may lead to undesired spectral components in transmitted signals, distortion of received signals, and interference between wanted signals and unwanted blocking signals in receivers. The component of distortion of greatest interest in many applications is the so called cubic or third-order distortion, which is often characterized by measuring an output third-order intercept point OIP3, that is, the output power at which an extrapolated third-order intermodulation product is equal to a fundamental output tone. Typically, a maximum OIP3 value indicates an optimal overall linearity. By both simulation and experiment, it is found that the RF frequency at which an optimal overall linearity is obtained in the prior-art circuit  400  of  FIG. 4  exhibits significant variations with temperature, as shown in  FIG. 5 . Such variations will result in inconsistent linearity at the frequency of operation as ambient temperature varies, which is unacceptable in many applications.  
       SUMMARY OF THE INVENTION  
       [0010]     It is an object of the invention to provide a microwave bipolar transistor amplifier with constant, well-controlled bias current, and consistently excellent linearity over a wide range of temperature, without degradation of power efficiency. It is a further object of the invention to provide means for adapting the dependency of linearity on frequency to the needs of any specific application, without requiring changes in the RF amplifier circuit configuration.  
         [0011]     An amplifier circuit according to one embodiment of the present invention comprises an amplifier transistor configured to amplify an input signal received at a terminal of the amplifier transistor, and a bias circuit having a bias transistor forming a current mirror with the amplifier transistor for stabilizing a bias operating point for the amplifier transistor, a buffer transistor coupled to the bias transistor and to the amplifier transistor, and a current source coupled to the buffer transistor and configured to generate a temperature-dependent current for injection into the buffer transistor. The buffer transistor provides a DC base current for the amplifier transistor and improves linearity of the amplifier transistor by creating a predistortion of the input signal. The current source injects the temperature-dependent current into the buffer transistor to adjust the extent of predistortion and to compensate for effects caused by variations in ambient conditions. The behavior of the current source is designed to vary the predistortion characteristics of the bias circuit to track and cancel the distortion characteristics of the amplifier circuit over temperature, resulting in temperature-independent enhanced linearity performance of the overall amplifier circuit. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0012]      FIG. 1  is a circuit schematic illustrating a conventional amplifier circuit employing a resistive voltage divider for base bias.  
         [0013]      FIG. 2  is a circuit schematic illustrating a conventional amplifier circuit having an added series bias resistor.  
         [0014]      FIG. 3  is a circuit schematic illustrating a conventional amplifier circuit employing a current mirror bias scheme.  
         [0015]      FIG. 4  is a circuit schematic illustrating a conventional amplifier circuit employing a current mirror with buffer transistor.  
         [0016]      FIG. 5  is a chart showing plots of output third-order intercept point vs. frequency, at three different ambient temperatures, for the conventional amplifier circuit shown in  FIG. 4 .  
         [0017]      FIG. 6  is a circuit schematic illustrating an amplifier circuit according to one embodiment of the present invention.  
         [0018]      FIG. 7  is a circuit schematic illustrating an example of a temperature-compensating current source in the amplifier circuit shown in  FIG. 6 .  
         [0019]      FIG. 8  is a circuit schematic of a PTAT (proportional-to-absolute-temperature) cell according to one embodiment of the present invention.  
         [0020]      FIG. 9  is a chart illustrating a temperature-compensating current source output I TC .  
         [0021]      FIG. 10  is a circuit schematic of a negative temperature coefficient current source according to an alternative embodiment of the present invention.  
         [0022]      FIG. 11  is a chart showing simulated results of OIP3 versus temperature incorporating the temperature-compensating current source according to one embodiment of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0023]     The operation of an amplifier circuit according to one embodiment of the present invention may be better understood with reference to  FIG. 6 . As shown in  FIG. 6 , the amplifier circuit  600  comprises a radio frequency (RF) bipolar junction transistor Q RF  having its base coupled to an input terminal “RF in” for receiving an RF input signal, its emitter coupled to ground, and its collector coupled to a power supply voltage V CC  and to a signal output terminal “RF out.” Circuit  600  may further comprise an inductor L 1  coupled between the collector of transistor Q RF  and V CC .  
         [0024]     Circuit  600  further comprises a bias circuit  610  including a bias bipolar transistor Q b1 , buffer transistor Q b2 , first and second bias resistors R b1  and R b2 , first and second base resistors R b3  and R b5 , a resistor R b4 , and a temperature-compensated current source I TC . Transistor Q b1  has its base coupled to the base of transistor Q RF  through first and second base resistors R b3  and R b5 , its collector coupled to V CC  through first bias resistor R b1 , and its emitter coupled to ground through second bias resistor R b2 . Transistor Q b2  has its base coupled to the collector of transistor Q b1  through resistor R b4 , its collector coupled to V CC , and its emitter coupled to a circuit node between first and second base resistors R b3  and R b5 . Bias circuit  610  may further comprise a capacitor C 1  coupled between the base and collector of transistor Q b1 . Current source I TC  is coupled to the circuit node between first and second base resistors R b3  and R b5 .  
         [0025]     The RF input signal, which may typically be at a frequency in the range of a few hundred MHz to many GHz, is applied to the base of the RF transistor Q RF . Generally, this connection will be DC-blocked using a capacitor or equivalent arrangement (not shown). In order for transistor Q RF  to provide reasonably linear amplification at high gain, a significant DC bias current I C  should flow through the transistor Q RF  and the inductor L 1 , if it is provided. The inductor L 1 , when provided, acts to isolate the supply voltage V CC  from variations in an RF current through transistor Q RF . In one embodiment, transistors Q RF , Q b1 , and Q b2 , resistors R b1 , R b2 , R b3 , R b4 , and R b5 , capacitor C 1 , and current source I TC  are part of an integrated circuit fabricated on a semiconductor substrate, as indicated by the dotted lines in  FIG. 6 . Inductor L 1  can be external to the integrated circuit, or it can be an on-chip inductor formed on the same substrate as the integrated circuit.  
         [0026]     An appropriate DC voltage to ensure proper bias current I C  is provided to the base of Q RF  through resistor R b5 , which acts to allow base current I B1  to flow to or from transistor Q RF  while partially isolating the remainder of the bias circuit  610  from the RF input signal. The resistance value of resistor R b5  is chosen to be small to avoid excessive DC voltage drop due to the flow of base current to or from transistor Q RF . Additional isolation of the base of transistor Q b1  from the RF signal is provided by resistor R b3 . Capacitor C 1  provides electrical stability and noise reduction in bias circuit  610 . As a non-limiting example, resistor R b5  is about 20-100 ohms, resistor R b3  is about 100-1000 ohms, and capacitor C 1  is about 1-3 pF. A reference current I R  through transistor Q b1  is set by resistors R b1  and R b2  in conjunction with the supply voltage V CC . A base-emitter voltage of transistor Q b1  self-adjusts to accommodate the requisite reference current I R  through transistor Q b1 . Buffer transistor Q b2  provides a source for the base current I B1  for transistor Q RF  through R b5  and for a base current I B2  for transistor Q b1  through R b3 .  
         [0027]     The RF input signal is also applied to the emitter of transistor Q b2  through resistor R b5 . Thus, a portion of the signal voltage appears across the base-emitter junction of transistor Q b2 . This junction acts as a nonlinear load conductance of approximately:  
                     σ   be     ≈       ⁢       ⅆ     I   e         ⅆ     V   be                     =       ⁢       ⅆ     ⅆ     V   be         ⁢     (         β   +   1     β     ⁢     I   c2       )                   ≈       ⁢       ⅆ     I   c2         ⅆ     V   be                     =       ⁢       ⅆ     ⅆ     V   be         ⁢     (       I   S     ⁢     ⅇ       qV   be     /   kT         )                   =       ⁢       q   kT     ⁢     I   S     ⁢     ⅇ       qV   be     /   kT                     =       ⁢       q   kT     ⁢     I   c2                     (   2   )             
 
 where σ be  is a base-emitter differential conductance associated with transistor Q b2 , I e  represents emitter current of transistor Q b2 , V be  is the base-emitter voltage of transistor Q b2 , β represents the beta value or current gain of transistor Q b2 , and I c2  represents collector current of transistor Q b2 . 
 
         [0028]     The differential conductance σ be  is linearly dependent on the collector current I c2  of transistor Q b2 , and exponentially dependent on the RF voltage in V be , as demonstrated by Eq. (2). The base-emitter junction capacitance of transistor Q b2  also varies with current, with an additional dependency on the frequency of the RF input signal. The nonlinear load associated with the buffer transistor Q b2  may cause a distortion in the RF input signal provided to transistor Q RF , which, under certain conditions, could cancel the distortion caused by the RF transistor Q RF , leading to improved linearity. Conditions under which the effect of the buffer transistor Q b2  can be beneficial needs to be established by detailed modeling or empirical investigation of the specific process and geometry under study. According to Eq. (2), a change in the current flowing in transistor Q b2  can change the nonlinear conductance σ be . Furthermore, significant current can be drawn from the emitter of transistor Q b2  to change its collector current and therefore the conductance σ be  with little effect on the reference current through transistor Q b1  and thus on the bias current I C  of the RF transistor Q RF .  
         [0029]     In one embodiment of the present invention, current source I TC  is included in the bias circuit to draw current from the emitter of transistor Q b2 , in order to compensate for undesirable variations of predistortion with temperature. Therefore, any well-controlled temperature-varying current source may be used to construct I TC , as long as the current source is fabricated in a manner that allows for tailored adjustments in the current-temperature relationship associated with the current source. Preferably, the current source I TC  should be able to operate relatively independently of variations in the power supply voltage and/or variations in component values caused by unintentional variations in either processes or materials used to fabricate the current source. The current-temperature relationship required to produce optimal amplifier linearity can be established empirically and/or by simulation for a given process and circuit design.  
         [0030]     As one example of the current source I TC ,  FIG. 7  illustrates an exemplary amplifier circuit  700  employing a temperature compensated predistortion bias circuit  710 , which includes an I TC  current source  720 . As shown in  FIG. 7 , I TC  current source  720  comprises transistors Q 8 , Q 9 , Q 10 , and Q 11 , which form a proportional-to absolute-temperature (PTAT) cell  730  for driving a mirror transistor Q 12 , which in turn controls a current source transistor Q 7 . I TC  current source  720  further comprises resistors R 7 , R 9 , R 14 , R 15 , and R 16 . Transistors Q 8  and Q 11  are serially connected with each other and with resistor R 9  between V CC  and ground, and transistors Q 9  and Q 10  are serially connected with each other and with resistor R 14  between V CC  and ground. The base of transistor Q 8  is coupled to the collector of transistor Q 9 , and the base of transistor Q 9  is coupled to the collector of transistor Q 8 . Transistor Q 12  has its base coupled to the base of transistor Q 9  and to the collector of transistor Q 8 , its emitter coupled to the ground through resistor R 14 , and its collector coupled to the collector of transistor Q 11 , which, together with the emitter of transistor Q 11 , is coupled to V CC  though transistor R 9 . The emitter of transistor Q 9  is coupled to the ground through resistor R 14 . Transistor Q 7  has its collector coupled to a circuit node between resistors R b5  and R b3 , its base coupled to the collector of transistor Q 12 , and its emitter coupled to the ground through resistor R 7 .  
         [0031]     The operation of the PTAT cell  730  may be better understood by reference to  FIG. 8 , which shows a PTAT cell  800  formed of four transistors Q p1 , Q p2 , Q p3 , and Q p4 , and a resistor R e , in a configuration similar to that of PTAT cell  730 , with transistor Q p1 , Q p2 , Q p3 , and Q p4  and resistor R e  in PTAT cell  800  in similar positions as those of transistors Q 8 , Q 9 , Q 11 , and Q 10  and resistor R 14  in PTAT cell  730 , respectively. Consider a loop from a circuit node P in PTAT cell  800 , as shown in  FIG. 8 , to the base of transistor Q p1  across the base-emitter junction of transistor Q p1 , from there to the base of transistor Q p4  across the base-emitter junction of transistor Q p4 , from there to the emitter of transistor Q p3  across the base-emitter junction of transistor Q p3 , from there to the emitter of transistor Q p2  across the base-emitter junction of transistor Q p2 , and from there back to the circuit node P after passing through resistor R e . General circuit theory dictates that the sum of voltages along this loop must be zero. Therefore: 
 
 V   be1   +V   be4   −V   be3   −V   be2   −I   c2   R   e =0   (3) 
 
 where V be1 , V be4 , V be3 , and V be2  are base-emitter voltages of transistors Q p1 , Q p4 . Q p3 , and Q p2 , respectively, and I c2  is a current through transistors Q p2  and Q p4 , neglecting the base currents. 
 
         [0032]     The voltage across each base-emitter junction has a logarithmic relation with the current flow through it due to the exponential current-voltage characteristic of the associated transistor operating in the forward active region. Let the saturation currents of transistors Q p1 , Q p2 , Q p3 , and Q p4  be I S1 , I S2 , I S3 , and I S4 , respectively, neglecting base currents, and using Eq. (1), Eq. (3) becomes:  
                   V   T     ⁢     ln   ⁡     (       I   c1       I   S1       )         +       V   T     ⁢     ln   ⁡     (       I   c2       I   S4       )         -       V   T     ⁢     ln   ⁡     (       I   c1       I   S3       )         -       V   T     ⁢     ln   ⁡     (       I   c2       I   S2       )         -       I   c2     ⁢     R   e         =   0           (   4   )             
 
 where I c1  is the current through transistors Q p1  and Q p3 , and V T =kT/q is defined as the thermal voltage. 
 
         [0033]     Solving Eq. (4) for I c2  results:  
               I   c2     =           V   T       R   e       ⁢     ln   ⁡     (         I   c1     ⁢     I   c2     ⁢     I   S3     ⁢     I   S2           I   S1     ⁢     I   S4     ⁢     I   c1     ⁢     I   c2         )         =         V   T       R   e       ⁢       ln   ⁡     (         I   S3     ⁢     I   S2           I   S1     ⁢     I   S4         )       .                 (   5   )             
 
         [0034]     Presuming that transistors Q p1 , Q p2 , Q p3 , and Q p4  are fabricated on a same semiconductor substrate using a same set fabrication process, their saturation currents should be very accurately proportional to the respective junction areas. Let the ratio of base-emitter junction areas of transistors Q p2 , Q p3 , and Q p4  to that of transistor Q p1  be A S2 , A S3 , and A S4 , respectively, I c2  becomes:  
               I   c2     =           V   T       R   e       ⁢     ln   ⁡     (           A   S3     ⁢     I   S1         I   S1       ⁢         A   S2     ⁢     I   S1           A   S4     ⁢     I   S1           )         =         V   T       R   e       ⁢       ln   ⁡     (         A   S3     ⁢     A   S2         A   S4       )       .                 (   6   )             
 
         [0035]     Therefore, from Eq. (6), it is observed that the collector current I c2  depends only on the junction area ratios A S2 , A S3 , and A S4  associated with transistors Q p1 , Q p2 , Q p3 , and Q p4  and the resistor value chosen for resistor R e , and not on the absolute magnitude of the saturation currents I S1 , I S2 , I S3 , and I S4 . Note that I c2  is linearly proportional to the absolute temperature through the thermal voltage V T , as the name of the PTAT cell indicates. Thus, for example, if the base-emitter junction area of Q p2  is chosen to be 4 times that of Q p1 , the base-emitter junction area of Q p3  twice that of Q p1 , and the base-emitter junction area of Q p4  the same as that of Q p1 , I c2  becomes:  
               I   c2     =           V   T       R   e       ⁢     ln   ⁡     (       2   ·   4     1     )         =         V   T       R   e       ⁢     ln   ⁡     (   8   )                   (   7   )             
 
         [0036]     Referring back to  FIG. 7 , in a non-limiting example, the base-emitter junction areas of transistors Q 8  and Q 10  are equal, and the base-emitter junction areas of transistors Q 9  and Q 11  are equal to each other but twice as large as those of transistors Q 8  and Q 10 , it can be shown that the current through the collector of transistor Q 10  is approximately:  
               I   c10     =           V   T       R   e       ⁢     ln   ⁡     (       2   ·   2     1     )         =         V   T       R   e       ⁢     ln   ⁡     (   4   )                   (   8   )             
 
         [0037]     Thus, neglecting the base currents, the current through transistors Q 9  and Q 10  is linearly proportional to temperature through V T  and nearly independent of supply voltage. It can also be shown that the voltage at the collector of transistor Q 11  is nearly independent of small variations in the supply voltage. Because the collector current I c10  is constant with respect to variations in the supply voltage V CC , the base-emitter voltage V be10  of transistor Q 10  is essentially constant. Thus, any variation δv 11  in the voltage V 11  at the collector of transistor Q 11  is immediately mirrored to the emitter of transistor Q 10 , which is connected to the collector of transistor Q 14  and to the base of transistor Q 8 . Treating transistor Q 8  as a transconductance amplifier, the change δI 11  in the collector current I c11  of transistor Q 11  due to this change in voltage is g m8 δv 11 , where g m8  represents the transconductance associated with transistor Q 8 . This change in current flows in series through transistor Q 11  and resistor R 9 . Thus, for a change δv cc  in supply voltage V CC , the corresponding change δv 11  in the voltage V 11  at the collector of transistor Q 11  can be solved as in the following.  
                     δ   ⁢           ⁢     v   11       =         δ   ⁢           ⁢     v   cc       -       R   9     ⁡     (     δ   ⁢           ⁢     I   11       )         =       δ   ⁢           ⁢     v   cc       -       R   9     ⁡     (       g   m11     ⁢   δ   ⁢           ⁢     v   11       )                         δ   ⁢           ⁢       v   11     ⁡     (     1   +       R   9     ⁢     g   m11         )         =     δ   ⁢           ⁢     v   cc                     δ   ⁢           ⁢     v   11       =         δ   ⁢           ⁢     v   cc         1   +       R   9     ⁢     g   m11           ⁢     &lt;&lt;   δ     ⁢           ⁢     v   cc                     (   9   )             
 
         [0038]     As a non-limiting example, if R 9  is approximately 1000 ohms, I C11  is approximately 2 mA, and transconductance g m8  is about (40)(2)=80 mS at room temperature so R 9 gm 11  is roughly (0.08)(1000)=80, any change δv CC  in supply voltage V CC  would be attenuated almost 100-fold at collector of transistor Q 11 . Thus, the voltage output from the collector of transistor Q 12  and the operation of the current source  720  are substantially independent of supply voltage over a wide range.  
         [0039]     If the resistance value of resistor R 16  is set to be equal to that resistor R 14 , the collector current of transistor Q 12  would mirror that of transistor Q 9  provided the transistors have the same or nearly the same configuration. If the resistors differ in value, to a first approximation, the current through Q 12  scales inversely as the ratio of R 16 /R 14  assuming the base-emitter voltage V be12  of transistor Q 12  remains approximately the same (since the current through a transistor has an exponential relationship with the base-emitter voltage). As a non-limiting example, R 14  is set to be approximately 20 ohms and R 16  is set to be approximately 100 ohms, so that the collector current of transistor Q 12  is nearly proportional to the absolute temperature but the dependency is much less than that of transistor Q 9 , as numerical solution of related transcendental equations shows that the current I c12  through transistor Q 12  would be about equal to the current I c9  through transistor Q 9  divided by 3.4, i.e., I c12 =I c9 /3.4. This current I c12  is then multiplied by the resistance value associated with resistor R 15  to produce a voltage that is inversely proportional to temperature and is used to drive the base of transistor Q 7 . The resulting voltage impressed across resistor R 7  through the base-emitter diode of transistor Q 7  produces a compensation current I TC , which is inversely proportional to temperature.  
         [0040]     Adjustment of the two resistors R 16  and R 15  allows considerable freedom to vary both the magnitude of the compensation current I TC  as well as its degree of dependency on temperature. In a non-limiting example, a 2-μm indium gallium phosphide based heterojunction bipolar transistor (InGaP HBT) process is used to fabricate the amplifier circuit  700 , and it is empirically found that the injected current I TC  should optimally be negligible for temperatures greater than room temperature, and increase approximately linearly as temperature is decreased. The correct characteristic is achieved by setting R 15  to be approximately 2900 ohms. The resulting current-temperature characteristic for I TC  is depicted in  FIG. 9 . In this example, the RF transistor Q RF  is a InGaP HBT having an emitter area of about 420 μm 2 . For different design of the bias circuit  710  and associated passive components, as shown in  FIG. 7 , and for different processes for fabricating circuit  700 , a different optimal relationship of injected current I TC  vs. temperature T may be appropriate. In most cases the desired injected current characteristic can be obtained from the above example after appropriate variations in the resistors R 7 , R 15 , and R 16 .  
         [0041]     The I TC  current source  720  in  FIG. 7  is just one example of implementing the current source I TC  in  FIG. 6 . As another example,  FIG. 10  illustrates a negative temperature coefficient current source  1000 , which may also be used as the I TC  current source in  FIG. 6 . As shown in  FIG. 10 , current source  1000  comprises resistors R 1 , R 2 , R 4 , and R 5  serially coupled with each other between V CC  and ground, a resistor R 3  coupled between a circuit node  1010  between resistor R 1  and R 2  and a circuit node  1020  between resistors R 4  and R 5 , a first transistor Q 1  having its base coupled to circuit node  1020 , its collector coupled to a circuit node  1030  between resistors R 2  and R 4 , and its emitter coupled to ground, resistors R 6  and R 7  serially coupled with each other between circuit node  1030  and ground, and a second transistor Q 2  having its base coupled to a circuit node  1040  between resistors R 6  and R 7 , its collector coupled to circuit node  1030  through a resistor R 8 , and its emitter coupled to ground. Current source  1000  further comprises a third resistor Q 3  having its base and collector tied with each other and coupled to a circuit node  1050  between resistor R 8  and transistor Q 2 , and a fourth transistor Q 4  coupled to the third transistor in a current mirror arrangement. The emitter of transistor Q 3  is coupled to ground through a resistor R 9 , and the emitter of transistor Q 4  is coupled to ground through a resistor R 10 .  
         [0042]     Resistors R 1 , R 2 , R 3 , R 4 , and R 5  and transistor Q 1  act as a voltage regulator such that the voltage at circuit node  1030  is stable through variations in the V CC . A positive temperature coefficient current I 2  is generated through transistor Q 2 , which current goes up with increased temperature. As a result, the voltage at circuit node  1050 , i.e., the collector of transistor Q 2 , goes down with increased temperature, and so does the current I 3  through transistor Q 3 . The current I 3  is mirrored and scaled in transistor Q 4  to result in the I TC  current through transistor Q 4  to be a negative temperature coefficient current that decreases with increased temperature. The current I TC  is injected into the buffer transistor Q b2  in  FIG. 6  to adjust the extent of predistortion created by the buffer transistor and to compensate for effects caused by variations in temperature. Current I TC  and its dependency on temperature in  FIG. 10  can be adjusted by adjusting the resistance values associated with resistors R 8 , R 9 , and R 10 .  
         [0043]     The simulated OIP3 performance of an example of amplifier circuit  600  using an I TC  current source similar to that depicted in  FIG. 10  is plotted in  FIG. 11 . As shown in  FIG. 11 , the frequency at which an optimal overall linearity performance of amplifier circuit  600  is obtained is fairly independent of temperature. The presence of the I TC  current source produces a temperature-dependent variation in the phase and amplitude of the predistortion frequency products generated by the non-linear characteristics of the base-emitter junction of the buffer transistor Q b2 . These predistortion products in turn cancel out distortion frequency products generated in the amplifier transistor Q RF , resulting in a temperature-independent overall amplifier linearity enhancement. Furthermore, because of the design of the current source I TC , these results are relatively independent of variations in the supply voltage V CC , and of variations of the absolute resistance values of the resistors in the current source, as long as the ratios of the resistance values are maintained.  
         [0044]     This invention has been described in terms of a number of embodiments, but this description is not meant to limit the scope of the invention. Numerous variations will be apparent to those with skill in the art, without departing from the spirit of the invention disclosed herein.