Amplifier for controlling linear gain of wide band using external bias
BACKGROUND OF THE INVENTION 
     The present invention relates to an amplifier and, more particularly, to an amplifier for controlling linear gain of wide band using external bias which controls the amplification gain at high frequencies of a wide band input signal and has good linear gain characteristics for high-frequency and large-input signal by adjusting an external bias. 
     In image processing systems such as video tape recorders and televisions, differential amplifiers as shown in FIG. 1A and 1B are normally employed to amplify high-frequency image signals. In these amplifiers two identical transistors Q1 and Q2 are symmetrically composed between positive and negative supply voltages V cc  and -V EE  and common emitter current IEE is a constant current source. Collector resistors R c  &#39;S of the transistors Q1 and Q2 are identical with each other, and emitter resistors R e  are also identical with each other. Then, an input signal Vin applied to the base of the transistor Q1 is amplified and provided through the collector resistors Rc as an output voltage V c . 
     On the other hand, the gain of the amplifier shown in FIG. 1A is determined as follows. Applying the Kirchhoff&#39;s voltage law to a loop including the base-emitter junctions of the transistors Q1 and Q2, the following equation is satisfied, 
     
         V.sub.in =V.sub.BE1 -V.sub.BE2                             ( 1) 
    
     where, V BE2 , and V BE2  are the base-emitter voltage drops of the transistors Q1 and Q2, respectively. 
     Eq.(1) can also be rewritten as follows, using the relationship I c  =I s  ##EQU1## where, V T  (=kT/q) is the thermal voltage and has a value of about 26 mV at 300° K, I s  is the reverse saturation current and has a value of about 2×10 nA/cm 2  at 300° K, and I c1  and I c2  are the collector currents of the transistors Q1 and Q2. 
     Assuming that the transistors Q1 and Q2 are identical with each other, i.e., I s1  =I s2 , then Eqs.(1) or (2) can be rewritten as, ##EQU2## Also, the following relation is satisfied, 
     
         I.sub.c1 =I.sub.c2 =αF.I.sub.EE                      ( 4) 
    
     where, αF is the current amplification ratio in common-base configuration and has a value of almost 1. 
     Thus, the collector currents I c1  and I c2  are given from Eqs. (3) and (4), by ##EQU3## 
     On the other hand, the output voltage V o1  from the transistor Q1 and the output voltage V o2  from the transistor Q2 are given by, respectively, 
     
         V.sub.o1 =V.sub.cc -I.sub.c1 ·R.sub.c             ( 7) 
    
     
         V.sub.o2 =V.sub.cc -I.sub.c2 ·R.sub.c             ( 8) 
    
     Then, the final differential output voltage V o  becomes, ##EQU4## 
     As expressed in Eq.(10), when the input voltage V in  is larger than V T , a large distortion is produced due to hyperbolic tangent characteristics and thereby the circuit shown in FIG. 1A is no longer used as an amplifier. 
     In order to compensate the distortion, resistors R e  are appended to both emitters of the transistors Q1 and Q2. Then, the linearity is improved, but in has still another problem that the voltage gain is reduced. 
     SUMMARY OF THE INVENTION 
     The present invention solves these problems and provides an amplifier for controlling linear gain of wide band which amplifies a high-frequency and large-input wide band signal without distortion, by using external bias. 
     Further, the present invention provides an amplifier for controlling linear gain of wide band which is able to control the amplification gain of the high-frequency input signal by external bias adjustment. 
     Further more, the present invention provides an amplifier for controlling linear gain of wide band which is able to maintain stable gain characteristics even at high-frequency range by external bias adjustment. 
     According to the present invention, there is provided an amplifier for controlling linear gain of wide band including an amplifier for high-frequency application, comprising a first voltage generator for generating a first fine voltage with the inverse hyperbolic tangent function of an external bias voltage, a first voltage-to-current converter for generating a first current which is the hyperbolic tangent function of the first fine voltage, thereby being proportional linearly to the external bias, a second voltage generator for generating a second fine voltage with the inverse hyperbolic tangent function of an input signal, a second voltage-to-current converter for controlling the first current by generating a second current which is the hyperbolic tangent function of the second fine voltage, thereby being proportional linearly to the input signal, and a current-to-voltage converter for converting the first current to a linear output voltage. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1A and 1B show conventional amplifier circuits. 
     FIG. 2 is a block diagram of an amplifier according to the present invention, and 
     FIG. 3 is a detailed circuit of a preferred embodiment of the amplifier in FIG. 2 according to the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The present invention will be now described in more detail with reference to accompanying drawings. FIG. 2 shows the block diagram of an amplifier according to the present invention, which comprises a first voltage generator 10 for producing a first fine voltage ΔV 1  with the inverse hyperbolic tangent (tanh -1 ) function of an external bias voltage V B  for gain compensation, a first voltage-to-current (V/I) converter 20 connected to the first voltage generator 10 for generating a first current I1 with the hyperbolic tangent function (tanh) of the first fine voltage, thereby being proportional linearly to the external bias voltage V B , a second voltage generator 30 for producing a second fine voltage ΔV 2  with the inverse hyperbolic tangent function of an input voltage V in , a second voltage-to-current converter 40 connected to the second voltage generator 30 for generating a second current I2 with the hyperbolic tangent function of the second fine voltage ΔV 2 , thereby being proportional linearly to the input voltage V in , and a current-to-voltage (I/V) converter 50 connected to the first voltage-to-current converter 20 for converting the first current I.sub. 1 to a linear output voltage V o . 
     The first voltage generator 10 receives the external bias voltage V B  for controlling amplification gain and generates the first fine voltage ΔV 1  with the inverse hyperbolic tangent function of V B . Since the external bias voltage V B  is a DC voltage having a predetermined variable range, the first fine voltage ΔV 1  does not exceed 1V. 
     The first voltage-to-current converter 20 converts the first fine voltage ΔV 1  to the first current I 1  with the hyperbolic tangent function of ΔV 1 . Thus, the first current I 1  is proportional linearly to the external bias voltage V B . 
     On the other hand, the second voltage generator 30 receives the high-frequency input signal V in  and generates the second fine voltage ΔV 2  with the inverse hyperbolic tangent function of V in . The second fine voltage ΔV 2  is proportional to the input voltage V in , but does not exceed 1V, similar to the first fine voltage ΔV1. 
     The second voltage-to-current converter 40 converts the second fine voltage ΔV 2  to the second current I 2  with the hyperbolic tangent function of ΔV 2 . Thus, the second current is proportional linearly to the input voltage V in . Also, if the second current I2 is varied, the external bias voltage V B  is varied and thereby the first current I 1  is also varied. Thus, the first and second currents I 1  and I 2  are dependent linearly on each other. 
     As described above, the first current I 1  is adjusted by the external bias voltage V B  and proportional linearly to the second current I2, and converted to the output voltage V o  by the current-to-voltage converter 50. The output voltage V o  is also proportional linearly to the first current I 1 . Accordingly, a desired gain is achieved by adjusting the external bias voltage V B  ; and the linearity of the amplifier is maintained stably regardless of the magnitude of the high-frequency input signal V in . 
     FIG. 3 is the detailed circuit showing the embodiment of FIG. 2 according to the present invention, which comprises first and second voltage generators 10 and 30, first and second voltage-to-current converters 20 and 40, and a current-to-voltage converter 50, identical to the configuration in FIG. 2. 
     The first voltage generator 10 comprises transistors 11 and 12 of which emitters are symmetrically connected to each constant current source I o1  and bases are connected to an external bias voltages V B  added to a first reference voltage V ref1  and a second reference voltage V ref2 , respectively, resistor 13 connected between the emitters of the transistors 11 and 12, and diodes 14 and 15 of which cathodes are respectively connected to the collectors of the transistors 11 and 12 and anodes are connected in common to a supply voltage V cc . 
     The first voltage-to-current converter 20 comprises transistors 21 and 22 connected between the supply voltage V cc  and to each constant current source I o2  for buffering the input signals applied to each base from the collectors of the transistors 11 and 12, and emitter-coupled transistors 23 and 24 for receiving the output voltages from the emitter nodes of the transistors 21 and 22 as differential input signals. 
     The second voltage generator 30 comprises transistors 31 and 32 of which emitters are symmetrically connected to each constant current source I o1  and bases are respectively connected to an input voltages V in  added to a third reference voltage V ref3  and a fourth reference voltage V ref4 , a resistor 33 connected between the emitters of the transistors 31 and 32, and diodes 34 and 35 of which cathodes are respectively connected to the collectors of the transistors 31 and 32 and bases are connected to each other, and a transistor 36 of which a base is connected to a fifth reference voltage V ref5  for providing a desired voltage to the common anode node of the diodes 34 and 35 by a constant voltage dropped from the supply voltage V cc . 
     The second voltage-to-current converter 40 comprises transistors 41 and 42 connected between the supply voltage V cc  and each constant current source I o2  for buffering the input signals applied to each base from the collectors of the transistors 31 and 32, and transistors 43 and 44 of which bases are respectively connected to the emitters of the transistors 41 and 42 and emitters are connected in common to a constant current source I BB . The collector of the transistor 43 is connected to the common-emitter node of the transistors 23 and 24, while that of the transistor 44 is connected to the supply voltage V cc . 
     The current-to-voltage converter 50 comprises only a resistor connected between the supply voltage V cc  and the collector of the transistor 24. All of the transistors in FIG. 3 are NPN type. Also, all of the diodes in FIG. 3 are formed by using NPN transistors, i.e., the base of the NPN transistor is used as the anode, and the collector and emitter are tied to be used as the cathode. 
     Now, the operation of the embodiment according to the present invention shown in FIG. 3, is described in more detail. 
     The input-to-output voltage gain V o  /V in  is determined by the following sequence. 
     Neglecting the base currents of the transistors 31 and 32, first, their collector currents become, respectively, 
     
         i.sub.c1 =I.sub.o1 +i.sub.x1                               (11) 
    
     
         i.sub.c2 =I.sub.o1 -i.sub.x1                               (12) 
    
     where, i c1 , i c2 , I o1 , and i x1  are the collector current of the transistor 31, the collector current of the transistor 32, the constant current source, and the current flowing through the resistor 33 connected between the emitters of the transistors 31 and 32, respectively. 
     Applying the kirchhoff&#39;s second law (voltage law) to a loop including the base-emitter junctions of the transistors 31 and 32, the input voltage V in  is expressed as, 
     
         V.sub.in =V.sub.BB1 -V.sub.BB2 +i.sub.x1 ·R.sub.x (13) 
    
     where, V BB1  and V BB2  are the base-emitter voltages of the transistors 31 and 32, respectively, and R x  is the value of the resistor 33 connected between the emitters of the transistors 31 and 32. 
     Eq.(14) can be rewritten as, ##EQU5## where, V T  is the thermal voltage and I s1  and I s2  are the reverse saturation currents of the transistors 31 and 32, respectively, as explained in Eq. (2). 
     If the transistors 31 and 32 are identical with each other, i.e., the base doping density and the geometrical size are the same, then Is1 is equal to Is2 and thus Eq. (14) can be reduced to, ##EQU6## 
     Dividing both sides of Eq. (15) by R x  and substituting Eq.(11) and (12), one obtains, ##EQU7## 
     If the first term on the right side of Eq. (16) becomes zero, V in  is dependent linearly on i x1 . 
     Differentiating the first term of Eq. (16) with respect to i x1 , in order to identify this substantially, the following equation is satisfied, ##EQU8## where, r e  is the small-signal dynamic resistance at the emitter node of the transistor. 
     If R x  &gt; r e1  +r e2 , then, Eq. (16) satisfies the linear relationship, i.e., V in  is dependent linearly on i x1 . Thus, Eq. (11) and (12) can be simplified to, ##EQU9## 
     Since i c1  and i c2  are different from each other as shown in Egs. (18) and (19), voltage drops across the diodes 34 and 35 are also different from each other. This difference between the diode voltage drops is applied between the bases of the transistors 43 and 44. Applying the Kirchhoff&#39;s second law, the following equation is satisfied, 
     
         ΔV.sub.z =V.sub.BE3 -V.sub.BE4                       (20) 
    
     where, V BE1  and V BE2  are the voltage drops across the diodes 34 and 35, respectively, and V 2  is the second fine voltage. Therefore, Eq. (20) can be rewritten as, ##EQU10## where, I s3  and I s4  are the reverse saturation current of the diodes 34 and 35, respectively, as described in Eq. (2). 
     Assuming that the diodes 34 and 35 are identical with each other, i.e., I s3  =I s4 , Eq. (21) is reduced to, ##EQU11## 
     Using the relationship ##EQU12## 
     Eq. (22) can be written as, ##EQU13## 
     Thus, the voltage drop difference between the diodes 34 and 35 is the inverse hyperbolic tangent function of the input voltage. The voltage drop difference, i.e., the second fine voltage ΔV 2  is buffered by the transistors 41 and 42 and next applied between the transistors 43 and 44, thereby determining their collector currents i c4  and i c3 . 
     Thus, the second fine voltage ΔV 2  can be rewritten as, ##EQU14## where, V BE5  and V BE6  are the base-emitter voltage of the transistors 44 and 43. 
     Assuming that the transistors 43 and 44 are identical with each other. Eq. (25) becomes, ##EQU15## also, the following relation is satisfied, 
     
         i.sub.c3 +i.sub.c4 =αF·I.sub.EE             (28) 
    
     where, I EE  is the constant current and αF is almost 1. 
     Thus, Eq. (28) is reduced to, 
     
         i.sub.c3 +i.sub.c4 =I.sub.EE                               (29) 
    
     From Eq. (27) and (29), the collector currents of the transistors 44 and 43 are given by, respectively, ##EQU16## 
     Then, the collector current difference ΔI c  is given by, ##EQU17## 
     That is, the collector current difference I c  is the hyperbolic tangent function of the second fine voltage ΔV 2 . 
     Substituting Eq. (22) into Eq. (31) gives, ##EQU18## 
     Similarly, the collector current i c5  of the transistor 24 becomes the function of the external bias voltage V B , by ##EQU19## where, I c1  &#39; is the constant emitter current source and R x  &#39; is the value of the resistor 13 connected between the emitters of the transistors 11 and 12. 
     Combining Eqs. (33) and (34), the collector current i c5  of the transistor 24 is given, as a function of V B  and V in , by ##EQU20## 
     Thus, the total gain A v  of the amplifier in FIG. 3 is given by, ##EQU21## where, V o  is the output voltage from the amplifier and R L  is the value of the output resistor 50. 
     The collector current i c4  of the transistor 43, expressed in Eq. (33), corresponds to the second current I2 in FIG. 2 and the collector current i c5  of the transistor 24 corresponds to the first current I1 in FIG. 2. Thus, the voltage gain of the amplifier composed as FIG. 3 is determined by the current and the resistance at the output terminal, as expressed in Eq. (36). 
     As described hereinabove, the amplifier for controlling linear gain of wide band according to the present invention can obtain the desired gain for the high-frequency and large-input signal without the distortion.