Abstract:
A low-noise, linearized double-balanced active mixer circuit is described, including a first input for a local oscillator (LO), a second input for an intermediate frequency (IF) signal, and an output for a resulting product radio frequency (RF) signal. The mixer circuit also includes a feedback transformer circuit for the purpose of improving the intermodulation (IM) performance. The lossless nature of the feedback topology gives the active mixer a lower noise figure (NF) characteristic than is realizable with conventional methods. The mixer circuit further includes an augmentation circuit for correcting the non-linear input resistance of the common-base transistor amplifier. According to a further embodiment, the augmentation circuit includes a common-emitter transistor amplifier circuit. According to a further embodiment the augmentation circuit includes a positive-feedback transistor amplifier circuit. According to a further embodiment the augmentation circuit includes a two-winding transformer.

Description:
This application is related to a pending application filed on Aug. 7, 1998 entitled “Active Double-Balanced Mixer with Embedded Linearization Amplifiers”, application Ser. No. 9/130,740, by the same inventor the contents of which are incorporated herein by reference. 
     This application is related to a pending application filed Jun. 23, 1999 entitled “Common-Base Transistor Amplifiers with Linearity Augmentation”, application Ser. No. 9/338,850, by the same inventor the contents of which are incorporated herein by reference. 
     This application is related to a pending application filed on Jun. 30, 1999 entitled “Lossless Feedback Transistor Amplifiers with Linearity Augmentation”, application Ser. No. 9/340,495, by the same inventor the contents of which are incorporated herein by reference. 
     This application is related to a pending application filed on Jul. 7, 1999 entitled “Lossless Feedback Double-Balanced Active Mixers”, application Ser. No. 9/349,224, by the same inventor the contents of which are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     Mixers are used in communications circuits for the purpose of generating a modulated carrier for transmission, demodulating a modulated carrier in reception, or converting a signal at some input intermediate frequency (IF) to another output radio frequency (RF) by multiplying two input signals and thereby generating a third. A number of mixer realizations, both passive and active, are known in the art, and double-balanced mixers are known particularly well due to their advantages in the suppression of unwanted spurious signals and the isolation of any one of three ports to the other two, there generally being two inputs and one output. The Gilbert Cell has been the most widely used active mixer circuit for performing the above tasks, usually incorporated within an integrated circuit. It does, however, possess certain limitations in terms of intermodulation (IM) distortion and noise figure (NF) that precludes it&#39;s use in communications systems having demanding performance specifications. The series-shunt feedback double-balanced active mixer delivers a much improved IM performance, but the lossy nature of the feedback topology does not improve the NF performance. The lossless feedback double-balanced active mixer overcomes the noise limitations of the series-shunt feedback active mixer, but still retains a significant source of IM distortion. The purpose of the present invention is to address the source of IM distortion in the lossless feedback double-balanced active mixer and significantly reduce it&#39;s impact on the mixer linearity. 
     Referring to FIG. 1, a schematic diagram of a lossless feedback double-balanced active mixer is shown in functional form. Here, the mixer is comprised of switching transistors  101 ,  102 ,  104 , and  105 , which are turned on (saturation) and off (cutoff) alternately by a differentially applied local oscillator (LO) signal. By this switching action, a pair of currents generated by driver transistors  103  and  106  are divided into four paths, there being two paths for each of two currents. The currents generated by driver transistors  103  and  106  are the result of an input intermediate frequency (IF) signal applied differentially to the input windings of a pair of feedback transformers  107  and  108 . The hybrid transformers  111  and  112  combine the four currents from switching transistors  101 ,  102 ,  104 , and  105 , creating a differential pair of feedback currents  119  and  120 , as well as an output RF signal  121 . The feedback currents  119  and  120  are coupled to the output windings of feedback transformers  107  and  108 , respectively, thereby forming a pair of lossless feedback amplifiers which serve to establish the conversion gain and improve the IM performance of the mixer. 
     Those familiar with the art will readily understand that the improved NF performance of the lossless feedback double-balanced active mixer is a result of the lack of additional noise sources in the embedding topology. This active mixer offers considerable advantages over the more traditional Gilbert Cell active mixer, especially in terms of signal-handling and performance variations over temperature due to the temperature dependency of the emitter resistance r e  of the driver transistors, and the tradeoffs that are encountered in receiver and transmitter system design. It further provides substantial NF improvement over the Gilbert Cell mixer and the series-shunt feedback mixer. 
     Those familiar with the art will also readily understand that the IM performance of the lossless feedback double-balanced active mixer is impaired by the nonlinear emitter resistance r e  of the driver transistors  103  and  106 . Although this mixer offers substantial advantages in IM performance over the more traditional Gilbert cell active mixer, the presence of the nonlinear driver transistor emitter resistance causes the IM performance of the lossless feedback double-balanced active mixer to be less than ideal. This resistance is also the principal cause of conversion gain variation with temperature. It has long been desirable that a mixer, either passive or active, be available that has improved IM and temperature performance, and at the same time has an improved NF performance without the expense of added power. 
     It is the purpose of this invention to further advance the art of feedback mixers by addressing the primary source of IM distortion present in the lossless feedback double-balanced active mixer, and to therefore provide an active mixer of markedly improved IM performance, while at the same time conserving power consumption and retaining the NF performance and overall sense of simplicity and cost effectiveness of the lossless feedback double-balanced active mixer. 
     SUMMARY OF THE INVENTION 
     A lossless feedback double-balanced active mixer circuit with improved intermodulation (IM) and noise figure (NF) performance is described which includes a pair of lossless feedback balanced active mixer circuits, each of which includes a differential pair of switching transistors which divide a controlled current into two paths at a rate determined by an input local oscillator (LO). A hybrid transformer in each lossless feedback balanced mixer, consisting of a centre-tapped primary winding and a secondary winding, combines the two currents to provide a recombined amplified IF signal and an output radio frequency (RF) signal. A third driver transistor in each lossless feedback active mixer circuit provides the controlled current, which is determined by an input intermediate frequency (IF) signal. Each lossless feedback active mixer circuit further includes a feedback transformer, comprised of an input winding and a tapped output winding, which compares the input IF signal with the recombined amplified IF signal from the hybrid transformers and applies the difference as a correction to the amplifying transistors, thereby completing a lossless feedback amplifier circuit and in turn improving the IM performance of the mixer circuit. An augmentation circuit is included which improves the IM performance still further. Since the feedback transformer introduces no significant sources of noise to the active mixer circuit, the NF of the of the lossless feedback active mixer circuit remains unimpaired beyond the NF of the transistors themselves. The connection of the secondary windings of the hybrid transformers of the lossless feedback active mixer circuits effectively cancels the output LO and IF signals and provides an output RF signal. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention is described in the schematics of FIGS. 1 to  10 , in which: 
     FIG. 1 schematically illustrates the existing prior art, commonly referred to as a lossless feedback double-balanced active mixer; 
     FIG. 2 schematically illustrates a common-base transistor amplifier; 
     FIG. 3 schematically illustrates the combination of an augmenting voltage amplifier and a common-base transistor amplifier; 
     FIG. 4 schematically illustrates the combination of an augmenting voltage amplifier and a lossless feedback double-balanced active mixer in accordance with the present invention, 
     FIG. 5 schematically illustrates the combination of a common-emitter augmenting amplifier and a common-base transistor amplifier; 
     FIG. 6 schematically illustrates the combination of a common-emitter augmenting amplifier and a lossless feedback double-balanced active mixer in accordance with the present invention; 
     FIG. 7 schematically illustrates the combination of an inverting positive feedback amplifier and a lossless feedback double-balanced active mixer in accordance with the present invention; 
     FIG. 8 schematically illustrates the combination of an augmenting transformer and a common-base transistor amplifier; and 
     FIG. 9 schematically illustrates the combination of an augmenting transformer and a lossless feedback double-balanced active mixer in accordance with the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Designers of radio communication receivers are always concerned with elements of system performance which includes, but is not limited to, intermodulation distortion (IM), noise figure (NF), and power consumption. Historically, the IM performance of communications receivers is improved by methods that invariably require additional power consumption. Amplification stages with feedback methods are widely used as they offer far better IM performance while consuming less power than those not employing feedback. The NF of communications receivers is determined by the NF performance of the first stages of the receiver, which usually have sufficiently low NF and suitable signal gain to overcome the IM and NF performance of the first mixer stage, which is traditionally the primary source of distortion and noise. This invention now presents a mixer circuit which achieves a markedly improved IM and NF performance without excessive power consumption by applying a feedback method widely used in amplifier design which introduces no significant noise sources in addition to those of the active devices themselves. The IM performance is further improved by introducing an augmentation circuit which corrects a significant source of IM distortion. 
     A typical lossless feedback double-balanced active mixer circuit is shown in FIG.  1 . Here, transistor  103  and transformer  107  form a lossless feedback amplifier on the left side, while transistor  106  and transformer  108  form a lossless feedback amplifier on the right side. Transistors  101  and  102  form a chopper for the left side and transistors  104  and  105  form a chopper for the right side. Hybrid transformer  111  combines the currents from transistors  101  and  102 , the sum of which appears at the centre tap while the difference appears at the secondary winding. A similar description can be made for the second hybrid transformer  112  on the right side. A differential input Intermediate Frequency (IF) signal connected to the input windings of transformers  107  and  108  generates a differential pair of input currents  113  and  114 :                I   113     =       I   Q     +       A   ×   Cos                   ω   S        t       R     i                 n                   (   1   )                 I   114     =       I   Q     -       A   ×   Cos                   ω   S        t       R     i                 n                   (   2   )                                
     where ω S  is the frequency and A is the amplitude of the input IF signal, I Q  is the quiescent bias current, and R in  is the input resistance which is defined as:                R     i                 n       =         M   +   N   +   1       M   2       ×     R   11               (   3   )                                
     where M and N are the turns ratios of the output windings of transformers  107  and  108 . These input currents are conducted to the emitters of a pair of driver transistors  103  and  106 , respectively, which in turn conduct the currents to a first differential pair of switching transistors  101  and  102  and a second differential pair of switching transistors  104  and  105 . A Local Oscillator (LO) signal applied differentially across the base terminals of the differential switching transistor pairs results in two differential pairs of output currents:                      I   115     =                  I   113     ×       1   -     Cos                   ω   L        t       2                   =                      I   Q     ×     (     1   -     Cos                   ω   L        t       )       2     +                                A   ×     [       Cos                   ω   S        t     -           Cos        (       ω   S     -     ω   L       )          t     +       Cos        (       ω   S     +     ω   L       )          t       2       ]         2   ×     R     i                 n                         (   4   )                       I   116     =                  I   113     ×       1   +     Cos                   ω   L        t       2                   =                      I   Q     ×     (     1   +     Cos                   ω   L        t       )       2     +                                A   ×     [       Cos                   ω   S        t     +           Cos        (       ω   S     -     ω   L       )          t     +       Cos        (       ω   S     +     ω   L       )          t       2       ]         2   ×     R     i                 n                         (   5   )                       I   117     =                  I   114     ×       1   +     Cos                   ω   L        t       2                   =                      I   Q     ×     (     1   +     Cos                   ω   L        t       )       2     -                                A   ×     [       Cos                   ω   S        t     -           Cos        (       ω   S     -     ω   L       )          t     +       Cos        (       ω   S     +     ω   L       )          t       2       ]         2   ×     R     i                 n                         (   6   )                       I   118     =                  I   114     ×       1   -     Cos                   ω   L        t       2                   =                      I   Q     ×     (     1   -     Cos                   ω   L        t       )       2     -                                A   ×     [       Cos                   ω   S        t     -           Cos        (       ω   S     -     ω   L       )          t     +       Cos        (       ω   S     +     ω   L       )          t       2       ]         2   ×     R     i                 n                         (   7   )                                
     where ω S  is the frequency of the input LO signal. If both hybrid transformers  111  and  112  have turns ratios of 1:1:1 (K=1), then the currents at the center taps of the hybrid transformers  111  and  112  are, respectively:                I   119     =         I   115     +     I   116       =       I   Q     +       A   ×   Cos                   ω   S        t       R     i                 n                     (   8   )                 I   120     =         I   117     +     I   118       =       I   Q     -       A   ×   Cos                   ω   S        t       R     i                 n                     (   9   )                                
     and the output signal current conducted to the load resistance R L  is:                      i   121     =       K   ×     (       I   115     -     I   116       )       -     K   ×     (       I   117     -     I   118       )                     =     2   ×   A   ×     K   2     ×           Cos        (       ω   S     -     ω   L       )          t     +       Cos        (     ω   +     ω   L       )          t         R     i                 n                         (   10   )                                
     which makes the output signal voltage equal to:                v   121     =     2   ×   A   ×     K   2     ×     R   L     ×           Cos        (       ω   S     -     ω   L       )          t     +       Cos        (       ω   S     +     ω   L       )          t         R     i                 n                   (   11   )                                
     The input currents I 113  and I 114  of transistors  103  and  106 , determined earlier by EQ. 1 and EQ. 2, respectively, result in error voltages at the emitters of transistors  103  and  106 , which are, respectively:                V   113     =         I   113     ×     (       r   e     +       r   bb         h   fe     +   1         )       ≅       I   113     ×     r   e103                 (   12   )                 V   114     =         I   114     ×     (       r   e     +       r   bb         h   fe     +   1         )       ≅       I   114     ×     r   e106                 (   13   )                                
     where the nonlinear input resistances r e103  and r e106  of the driver transistors  103  and  106  are determined, respectively, by:                r   e103     =         V   113       I   113       =       V   113         I   O     ×            qV   113     kT                     (   14   )                 r   e106     =         V   114       I   114       =       V   114         I   O     ×            qV   114     kT                     (   15   )                                
     These nonlinear resistances are the primary cause of nonlinear distortion in the lossless feedback double-balanced mixer, and their reduction is essential to improving the linearity of the circuit. While they can be reduced partially by increasing the quiescent bias current I Q , it is preferable that other means not requiring substantial increases in power consumption be applied. 
     Referring to FIG. 2, a circuit commonly referred to as a common-base transistor amplifier circuit  200  is shown in its most basic form. Here, a transistor  205  has its base connected to ground, hence the term common-base. A resistance  203  (illustrated as a fixed resistance R E  for convenience), is connected from a signal voltage source  201 , having an amplitude A and a frequency of ω S , to an emitter of transistor  205 . A collector of transistor  205  is connected through a load resistance  207  (illustrated as a fixed resistance R L  for convenience) to a common point, such as ground. An output voltage  206  is described by the equation: 
     
       
           V   206   =I   C   ×R   L    (16)  
       
     
     where I C  is the instantaneous collector current of transistor  205 . This collector current is related to the input emitter current I E  by the equation:                I   C     =         I   E     ×     h   fe           h   fe     +   1               (   17   )                                
     where h fe  is the signal current gain of transistor  205 . The input emitter current I E  is a result of the input signal voltage at  202  and the input resistance R in , which is approximately described by:                R     i                 n       =         R   E     +     r   e     +       r   bb         h   fe     +   1         ≅       R   E     +     r   e                 (   18   )                                
     where r bb  is the base spreading resistance and r e  is the nonlinear incremental emitter resistance of transistor  205 , the latter of which is described by:                r   e     =         V   BE       I   E       =       V   BE         I   O     ×            qV   BE     kT                     (   19   )                                
     where I O  is the saturation current and V BE  is the base-emitter voltage of transistor  205 , the latter of which is equal to −V 204 . This voltage constitutes an error voltage  204  at the emitter of transistor  205 , which can be described as:                V   204     =       V   202     ×       r   e         R   E     +     r   e                   (   20   )                                
     Examination of EQ. 18 and EQ. 20 shows that as the emitter resistance term is reduced, the input resistance R in  more closely approximates the fixed emitter resistance R E . This, in turn, reduces the emitter error voltage V 204 , thus linearizing the input resistance R E  and the input current I E , which results in a linear collector current and thus linearizes the amplifier. Similarly, reducing the emitter error voltage V 204,  creating a virtual ground at the emitter terminal of transistor  205 , has the same effect. 
     Turning now to FIG. 3, a circuit commonly known as an augmented common-base transistor amplifier circuit  300  is illustrated. Circuit  300  includes an input signal source  301 , supplying an input signal voltage  302 , which is coupled through a resistance  303  (illustrated as a fixed resistance R E  for convenience) to the emitter of a transistor  305 . An augmentation circuit including an inverting voltage amplifier  306  has an input connected to the emitter of transistor  305  and an output connected to the base of transistor  305 . The collector of transistor  305  produces an output voltage  308  across a load resistance  309  (illustrated as a fixed resistance R L  for convenience), the opposite end of which is connected to a common point, such as ground. It will of course be understood that in accordance with common practice the input signal source  301  and the load resistance  309  represent any convenient input and output apparatus, respectively. The augmentation amplifier  306  has an inverting voltage gain factor of −A V , producing an amplified error voltage  307 , which is applied to the base of transistor  305 . This voltage is described as: 
     
       
           V   307   =−A   V   ×V   304    (21)  
       
     
     where V 304  is the is the emitter voltage  304 . The resulting base-emitter voltage V BE  of transistor  305  becomes: 
     
       
           V   BE   =V   307   −V   304   =−A   V   ×V   307   −V   304   =−V   304 ×( A   V +1)   (22)  
       
     
     Substituting EQ. 22 into EQ. 19, we find that the apparent emitter resistance r e ′ becomes:                r   e   ′     =         V   304       I   E       =         V   304         I   O     ×              qV   304     ×     (       A   V     +   1     )       kT           =       V   BE         (       A   V     +   1     )     ×     I   O                 qV   BE     kT                       (   23   )                                
     Referring now to FIG. 4, an embodiment of an augmented lossless feedback double-balanced active mixer circuit in accordance with the present invention, designated  400 , is illustrated. Here, transistor  403  and transformer  407  form a lossless feedback amplifier on the left side, while transistor  406  and transformer  408  form a lossless feedback amplifier on the right side. A differential pair of input currents  413  and  414  are conducted to the emitters of driver transistors  403  and  406 , respectively, which in turn are conducted to a first differential pair of switching transistors  401  and  402  and second differential pair of switching transistors  404  and  405 . Hybrid transformer  411  combines the currents  415  and  416  from transistors  401  and  402 , the sum of which appears as a feedback current  419  at a centre tap while the difference appears at a secondary winding. Similarly, hybrid transformer  412  combines the currents  417  and  418  from transistors  404  and  405 , the sum of which appears as a feedback current  420  at a centre tap while the difference appears at a secondary winding. 
     The two output currents from the secondary windings of hybrid transformers  411  and  412  are combined to form an output voltage  421  across an output load resistance  422  (illustrated as a fixed resistance R L  for convenience). The feedback current  419  is conducted to an output winding of feedback transformer  407 , where a resistor  409  (illustrated as a fixed resistance R 41  for on-venience) serves to terminate the first amplified IF signal. Similarly, the feedback current  420  is conducted to an output winding of feedback transformer  408 , where a resistor  410  (illustrated as a fixed resistance R 41  for convenience) serves to terminate the second amplified IF signal. 
     A differential input Intermediate Frequency (IF) signal connected to the input windings of transformers  407  and  408  generates the differential pair of input currents  413  and  414 :                I   413     =       I   Q     +       A   ×   Cos                   ω   S        t       R     i                 n                   (   24   )                 I   414     =       I   Q     -       A   ×   Cos                   ω   S        t       R     i                 n                   (   25   )                                
     where ω S  is the frequency and A is the amplitude of the input IF signal, I Q  is the quiescent bias current, and R in  is the input resistance which is defined as:                R     i                 n       =         M   +   N   +   1       M   2       ×     R   41               (   26   )                                
     where M and N are the turns ratios of the output windings of transformers  407  and  408 . These input currents result in a differential pair of nonlinear error voltages at the emitters of transistors  403  and  406 :                v   413     =         i   413     ×     (       r   e     +       r   bb         h   fe     +   1         )       ≅       i   413     ×     r   e403   ′                 (   27   )                 v   414     =         i   414     ×     (       r   e     +       r   bb         h   fe     +   1         )       ≅       i   414     ×     r   e406   ′                 (   28   )                                
     where r′ e403  and r′ e406  are the apparent emitter input resistances of the driver transistors  403  and  406 , respectively. Assuming that the augmentation amplifiers  423  and  425  have equal voltage gain factors of −A V , the amplified error voltages  424  and  426  at the bases of transistors  403  and  406  are, respectively: 
     
       
         ν 424   =−A   V ×ν 413    (29)  
       
     
     
       
         ν 426   =−A   V ×ν 414    (30)  
       
     
     Substituting EQ. 29 and EQ. 30 into EQ. 23, the equivalent emitter resistances of transistors  403  and  406  are, respectively:                r   e403   ′     =         V   413       I   413       =         V   413         I   O     ×              qV   413     ×     (       A   V     +   1     )       kT           =       V   BE         (       A   V     +   1     )     ×     I   O     ×            qV   BE     kT                       (   31   )                 r   e406   ′     =         V   414       I   414       =         V   414         I   O     ×              qV   414     ×     (       A   V     +   1     )       kT           =       V   BE         (       A   V     +   1     )     ×     I   O     ×            qV   BE     kT                       (   32   )                                
     thus showing that the inclusion of the augmenting voltage amplifiers  423  and  425  in the lossless feedback double-balanced active mixer circuit  400  of FIG. 4 achieves the necessary condition for improving the linearity of the circuit. From inspection of EQ. 31 and 32 it can be seen that the apparent emitter resistance r e ′ is greatly reduced as the voltage gain A V  of augmentation amplifiers  423  and  425  are increased, and that the input resistance becomes more closely equal to the fixed input resistance R E  as the voltage gain is increased, thus showing that the addition of augmentation amplifiers  423  and  425  have caused the emitter terminals of transistors  403  and  406 , respectively, to appear as virtual grounds, thus achieving the necessary condition discussed earlier for linearizing a lossless feedback double-balanced active mixer. 
     In some applications, particularly those at higher frequencies, the use of augmentation amplifiers  423  and  425  as shown in FIG. 4 may be impractical. Referring to FIG. 5, an augmented common-base transistor amplifier circuit  500 , employing a common-emitter transistor amplifier for augmentation, is illustrated. Circuit  500  includes an input signal voltage source  501 , supplying an input signal voltage  502 , which is coupled through a resistance  503  (illustrated as a fixed resistance R E  for convenience) to the emitter of a transistor  505 . An augmentation circuit including a common-emitter transistor amplifier  506  has a base connected to the emitter of transistor  505 , a grounded or common emitter, and a collector connected to the base of transistor  505 , which produces a base voltage  507  of transistor  505 . The collector of transistor  505  produces an output voltage  508  across a load resistance  509  (illustrated as a fixed resistance R L  for convenience), the opposite end of which is connected to a common point, such as ground. It will of course be understood that in accordance with common practice the input signal source  501  and the load resistance  509  represent any convenient input and output apparatus, respectively. In this case, the input current at the emitter of transistor  505  is described as:                      I   E   ′     =       I   E1     +     I   B2                   =         I   B1     ×     (       h   fe1     +   1     )       +       I   B1       h   fe2                     =       (       h   fe1     +   1   +     1     h   fe2         )     ×     I   O2     ×            qV   BE     kT                       (   33   )                                
     where h fe1  is the signal current gain of transistor  505 , h fe2  is the signal current gain of transistor  506 , I O2  is the saturation current of transistor  506 , and V BE  is the base-emitter voltage of transistor  505 . Substituting EQ. 33 into EQ. 19, we find that the apparent emitter resistance r e ′ becomes approximately:                r   e   ′     =         V   504       I   E   ′       =       V   504         (       h   fe1     +   1   +     1     h   fe2         )     ×     I   O2     ×            qV   BE     kT                     (   34   )                                
     which is a considerable reduction in the nonlinear emitter resistance of the common-base transistor amplifier, and thus showing that the use of common-emitter transistor amplifier  506  fulfills the requirements for linearizing the common-base transistor amplifier circuit  200  of FIG.  2 . 
     Referring now to FIG. 6, an embodiment of an augmented lossless feedback double-balanced active mixer circuit in accordance with the present invention, designated  600 , is illustrated. Here, transistor  603  and transformer  607  form a lossless feedback amplifier on the left side, while transistor  606  and transformer  608  form a lossless feedback amplifier on the right side. A differential pair of input currents  613  and  614  are conducted to the emitters of driver transistors  603  and  606 , respectively, which in turn are conducted to a first differential pair of switching transistors  601  and  602  and second differential pair of switching transistors  604  and  605 . Hybrid transformer  611  combines the currents  615  and  616  from transistors  601  and  602 , the sum of which appears as a feedback current  619  at a centre tap while the difference appears at a secondary winding. Similarly, hybrid transformer  612  combines the currents  617  and  618  from transistors  604  and  605 , the sum of which appears as a feedback current  620  at a centre tap while the difference appears at a secondary winding. 
     The two output currents from the secondary windings of hybrid transformers  611  and  612  are combined to form an output voltage  621  across the output load resistance  622  (illustrated as a fixed resistance R L  for convenience). The feedback current  619  is conducted to an output winding of feedback transformer  607 , where a resistor  609  (illustrated as a fixed resistance R 61  for convenience) serves to terminate the first amplified IF signal. Similarly, the feedback current  620  is conducted to an output winding of feedback transformer  608 , where a resistor  610  (illustrated as a fixed resistance R 61  for convenience) serves to terminate the second amplified IF signal. 
     A differential input Intermediate Frequency (IF) signal connected to the input windings of transformers  607  and  608  generates the differential pair of input currents  613  and  614 :                I   613     =       I   Q     +       A   +     Cos                   ω   S        t         R     i                 n                   (   35   )                 I   614     =       I   Q     -       A   ×   Cos                   ω   S        t       R     i                 n                   (   36   )                                
     where ω S  is the frequency and A is the amplitude of the input IF signal, I Q  is the quiescent bias current, and R in  is the input resistance which is defined as:                R     i                 n       =         M   +   N   +   1       M   2       ×     R   61               (   37   )                                
     where M and N are the turns ratios of the output windings of transformers  607  and  608 . These input currents result in a differential pair of nonlinear error voltages at the emitters of transistors  603  and  606 :                v   613     =         i   613     ×     (       r   e     +       r   bb         h   fe     +   1         )       ≅       i   613     ×     r   e603   ′                 (   38   )                 v   614     =         i   614     ×     (       r   e     +       r   bb         h   fe     +   1         )       ≅       i   614     ×     r   e606   ′                 (   39   )                                
     where r′ e603  and r′ e606  are the apparent emitter input resistances of the driver transistors  603  and  606 , respectively. Assuming that the augmentating common-emitter transistor amplifiers  623  and  625  have similar characteristics, the input currents at the emitters of transistors  603  and  606  are:                      I   E603   ′     =       I   E603     +     I   B623                   =         I   B623     ×     (       h   fe1     +   1     )       +       I   B623       h   fe2                     =       (       h   fe1     +   1   +     1     h   fe2         )     ×     I   O2     ×            qV   BE     kT                       (   40   )                       I   E606   ′     =       I   E606     +     I   B625                   =         I   B625     ×     (       h   fe1     +   1     )       +       I   B625       h   fe2                     =       (       h   fe1     +   1   +     1     h   fe2         )     ×     I   O2     ×            qV   BE     kT                       (   41   )                                
     where h fe1  is the signal current gain of transistors  603  and  606 , h fe2  is the signal current gain of transistors  623  and  625 , I O2  is the saturation current of transistors  623  and  625 , and V BE  is the base-emitter voltage of transistors  623  and  625 . Substituting EQ. 40 and EQ. 41 into EQ. 14 and EQ. 15, the equivalent emitter resistances of transistors  603  and  606  are, respectively:                r   e603   ′     =         V   613       I   E603   ′       =       V   BE         (       h   fe1     +   1   +     1     h   fe2         )     ×     I   O2     ×            qV   BE     kT                     (   42   )                 r   e606   ′     =         V   614       I   E606   ′       =       V   BE         (       h   fe1     +   1   +     1     h   fe2         )     ×     I   O2     ×            qV   BE     kT                     (   43   )                                
     thus showing that the inclusion of the augmenting common-emitter transistor amplifiers  623  and  625  to the lossless feedback double-balanced active mixer circuit  600  of FIG. 6 achieves the necessary condition for improving the linearity of the circuit. 
     For applications where higher degrees of linearity are required, the voltage gain of the augmenting common-emitter transistor amplifiers can be increased by providing a means of positive feedback. Referring specifically to FIG. 7, an embodiment of an augmented lossless feedback double-balanced active mixer circuit in accordance with the present invention, designated  700 , is illustrated. Here, transistor  703  and transformer  707  form a lossless feedback amplifier on the left side, while transistor  706  and transformer  708  form a lossless feedback amplifier on the right side. A differential pair of input currents  713  and  714  are conducted to the emitters of driver transistors  703  and  706 , respectively, which in turn are conducted to a first differential pair of switching transistors  701  and  702  and second differential pair of switching transistors  704  and  705 . Hybrid transformer  711  combines currents  715  and  716  from transistors  701  and  702 , the sum of which appears as a feedback current  719  at a centre tap while the difference appears at a secondary winding. Similarly, hybrid transformer  712  combines currents  717  and  718  from transistors  704  and  705 , the sum of which appears as a feedback current  720  at a centre tap while the difference appears at a secondary winding. 
     The two output currents from the secondary windings of hybrid transformers  711  and  712  are combined to form an output voltage  721  across an output load resistance  722  (illustrated as a fixed resistance R L  for convenience). The feedback current  719  is conducted to an output winding of feedback transformer  707 , where a resistor  709  (illustrated as a fixed resistance R 71  for convenience) serves to terminate the first amplified IF signal. Similarly, the feedback current  720  is conducted to an output winding of feedback transformer  708 , where a resistor  710  (illustrated as a fixed resistance R 71  for convenience) serves to terminate the second amplified IF signal. 
     The two input currents  713  and  714  induce error voltages at the emitters of driver transistors  703  and  706 , respectively. A positive feedback augmentation amplifier consisting of a transistor  724  and a transformer  723  amplifies the error voltage at the emitter of driver transistor  703 , which then conducts an amplified signal current  725  to the base of driver transistor  703 , thereby providing an augmentation circuit of very high gain for the left side of the augmented lossless feedback double-balanced mixer circuit. Similarly, a positive feedback augmentation amplifier consisting of a transistor  727  and a transformer  726  amplifies the error voltage at the emitter of driver transistor  706 , which then conducts an amplified signal current  728  to the base of driver transistor  706 , thereby providing an augmentation circuit of very high gain for the right side of the augmented lossless feedback double-balanced active mixer circuit. 
     It will be recognized by those familiar to the art that the positive feedback amplifier represented by transistor  724  and transformer  723  and the positive feedback amplifier represented by transistor  727  and transformer  726  are but one of many methods by which a positive feedback amplifier suitable for augmentation may be realized. 
     For applications at high frequencies and especially where the noise figure (NF) is a concern, an augmentation circuit including an active element such as a common-emitter transistor amplifier may be impractical. Referring specifically to FIG. 8, an augmented common-base transistor amplifier circuit, designated  800 , using a simple transformer is illustrated. Circuit  800  includes an input voltage source  801 , supplying an input signal voltage  802 , which is coupled through a resistance  803  (illustrated as a fixed resistance R E  for convenience) to the emitter of a transistor  805 . An augmentation circuit including a transformer  806  has a primary winding connected between the emitter of transistor  805  and a common point, such as ground. A secondary winding of transformer  806  is connected, in reverse phase relative to the primary winding, between the base of transistor  805  and the common or ground, producing a base voltage  807 . The collector of transistor  805  produces an output voltage  808  across a load resistance  809  (illustrated as a fixed resistance R L  for convenience), the opposite end of which is connected to a common point, such as ground. It will of course be understood that in accordance with common practice the input signal source  801  and the load resistance  809  represent any convenient input and output apparatus, respectively. The base-emitter voltage V BE , being the difference between base voltage  807  and emitter voltage  804 , and the base current I B  for circuit  800  are, respectively:                V   BE     =         V   807     -     V   804       =           -   L     ×     V   804       -     V   804       =       -     V   804       ×     (     L   +   1     )                   (   44   )                 I   B     =       I   E       h   fe               (   45   )                                
     where L is the turns ratio of the secondary winding to the primary winding of transformer  806 . This makes the input current I E ′ equal to:                I   E   ′     =         I   E     -       L   ×     I   E         h   fe         =       I   E     ×     (     1   -     L     h   fe         )                 (   46   )                                
     where                I   E     =         I   O     ×              q        (     1   +   L     )            V   404       kT         =       I   O     ×       [            qV   404     kT       ]       (     1   +   L     )                   (   47   )                                
     which allows the apparent emitter resistance r e ′ to be approximated as:                      r   e   ′     =       V   804       I   E805   ′                   =       V   804         (     1   -     L     h   fe         )     ×     I   O     ×              q        (     L   +   1     )            V   804       kT                       =       V   BE         (     L   +   1     )     ×     (     1   -     L     h   fe         )     ×     I   O     ×            qV   BE     kT                         (   48   )                                
     which, compared to EQ. 19, shows that the apparent emitter resistance r e ′ decreases dramatically as the turns ratio L of transformer  806  is increased, showing that the use of augmentation transformer  806  fulfills the requirements for linearizing the common-base transistor amplifier circuit  800  of FIG.  8 . 
     Referring now to FIG. 9, an embodiment of an augmented lossless feedback double-balanced active mixer circuit in accordance with the present invention, designated  900 , is illustrated. Here, transistor  903  and transformer  907  form a lossless feedback amplifier on the left side, while transistor  906  and transformer  908  form a lossless feedback amplifier on the right side. A differential pair of input currents  913  and  914  are conducted to the emitters of driver transistors  903  and  906 , respectively, which in turn are conducted to a first differential pair of switching transistors  901  and  902  and second differential pair of switching transistors  904  and  905 . Hybrid transformer  911  combines currents  915  and  916  from transistors  901  and  902 , the sum of which appears as a feedback current  919  at a centre tap while the difference appears at a secondary winding. Similarly, hybrid transformer  912  combines currents  917  and  918  from transistors  904  and  905 , the sum of which appears as a feedback current  920  at a centre tap while the difference appears at a secondary winding. 
     The two output currents from the secondary windings of hybrid transformers  911  and  912  are combined to form an output voltage  921  across an output load resistance  922  (illustrated as a fixed resistance R L  for convenience). The feedback current  919  is conducted to an output winding of feedback transformer  907 , where a resistor  909  (illustrated as a fixed resistance R 91  for convenience) serves to terminate the first amplified IF signal. Similarly, the feedback current  920  is conducted to an output winding of feedback transformer  908 , where a resistor  910  (illustrated as a fixed resistance R 91  for convenience) serves to terminate the second amplified IF signal. 
     A differential input Intermediate Frequency (IF) signal connected to the input windings of transformers  907  and  908  generates the differential pair of input currents  913  and  914 :                I   913     =       I   Q     +       A   ×   Cos                   ω   S        t       R     i                 n                   (   49   )                 I   914     =       I   Q     -       A   ×   Cos                   ω   S        t       R     i                 n                   (   50   )                                
     where ω S  is the frequency and A is the amplitude of the input IF signal, I Q  is the quiescent bias current, and R in  is the input resistance which is defined as:                R     i                 n       =         M   +   N   +   1       M   2       ×     R   91               (   51   )                                
     where M and N are the turns ratios of the output windings of transformers  907  and  908 . These input currents result in a differential pair of nonlinear error voltages at the emitters of transistors  903  and  906 :                v   913     =         i   913     ×     (       r   e     +       r   bb         h   fe     +   1         )       ≅       i   913     ×     r   e903   ′                 (   52   )                 v   914     =         i   914     ×     (       r   e     +       r   bb         h   fe     +   1         )       ≅       i   914     ×     r   e906   ′                 (   53   )                                
     where r′ e903  and r′ e906  are the apparent emitter input resistances of the driver transistors  903  and  906 , respectively. Assuming that the augmenting transformers  923  and  925  have similar characteristics, the input currents at the emitters of transistors  903  and  906  are:                I   E903   ′     =         I   E903     -       L   ×     I   E903         h   fe         =       I   E903     ×     (     1   -     L     h   fe         )                 (   54   )                 I   E906   ′     =         I   E906     -       L   ×     I   E906         h   fe         =       I   E906     ×     (     1   -     L     h   fe         )                 (   55   )                                
     where h fe  is the signal current gain of transistors  903  and  906 , and L is the turns ratios of the augmentation transformers  923  and  925 . The base-emitter voltages for transistors  903  and  906  are: 
     
       
           V   BE903   =V   924   −V   913   =−L×V   913   −V   913   =−V   913 ×( L+ 1)   (56)  
       
     
     
       
           V   BE906   =V   926   −V   914   =−L×V   914   −V   914   =−V   914 ×( L+ 1)   (57)  
       
     
     Substituting EQ. 54 and EQ. 56 into EQ. 14 and substituting EQ. 55 and EQ. 57 into EQ. 15, the equivalent emitter resistances of transistors  903  and  906  are, respectively:                      r   e903   ′     =       V   913       I   E903   ′                   =       V   913         (     1   -     L     h   fe         )     ×     I   O     ×              q        (     L   +   1     )            V   913       kT                       =       V   BE         (     L   +   1     )     ×     (     1   -     L     h   fe         )     ×     I   O     ×            qV   BE     kT                         (   58   )                       r   e906   ′     =       V   914       I   E906   ′                   =       V   914         (     1   -     L     h   fe         )     ×     I   O     ×              q        (     L   +   1     )            V   906       kT                       =       V   BE         (     L   +   1     )     ×     (     1   -     L     h   fe         )     ×     I   O     ×            qV   BE     kT                         (   58   )                                
     thus showing that the inclusion of the augmenting transformers  923  and  925  to the lossless feedback double-balanced active mixer circuit  900  of FIG. 9 achieves the necessary condition for improving the linearity of the circuit. 
     Although detailed embodiments of the invention have been described, it should be appreciated that numerous modifications, variations, and adaptations may be made without departing from the scope of the invention as described in the claims. For example, those familiar with the art will recognize that the bipolar transistors shown in the embodiments may be alternatively replaced with field effect transistors. Also, the single-transformer lossless feedback topology shown in the embodiments may be alternatively replaced with other forms of lossless feedback that are known to the art. 
     Further, while the terminals of the bipolar transistors described in the various embodiments are referred to as the emitter, base, and collector, it will be understood that these terminals will be the source, gate, and drain when the transistors utilized are field effect transistors or other similar types and may be referred to as input, control and output terminals, respectively, however the titles of the various components and terminals are only intended to enhance the understanding of the disclosure and are not intended to in any way limit the type of component utilized. In addition, it should be understood that the terms “lossless feedback transformer” and “hybrid transformer” used throughout this disclosure refer to general types of transformers and should not be limited in any way to specific types of transformers.