Variable gain amplifier with a gain exhibiting a linear in dB characteristic relative to a control voltage

1. Field of the Invention

The present invention relates generally to variable gain amplifiers and particularly to linear gain amplifiers.

2. Description of the Background Art

FIG. 5 shows a variable gain amplifier configured of an amplification circuit 100 and a control circuit 400 controlling a gain of amplification circuit 100 . Amplification circuit 100 is configured, as described hereinafter. Amplification circuit 100 includes n-channel MOS transistors M 1 -M 6 (first to sixth MOS transistors, respectively), and load resistances Z1 and Z2 (first and second load resistances, respectively). Herein, transistors M 1 and M 2 are identical in characteristics, and so are transistors M 3 and M 4 , and transistors M 5 and M 6 . Herein, “identical in characteristics” means “equal in threshold voltage, gain constant, transconductance provided when a uniform current flows, and in drain resistance.”

Transistors M 3 and M 5 have their respective drains connected together at a point connected to a first output terminal. Transistors M 4 and M 6 have their respective drains connected together at a point connected to a second output terminal. Transistors M 3 and M 4 have their respective sources connected together at a point connected to transistor M 2 at the drain.

Transistors M 5 and M 6 have their respective sources connected together at a point connected to transistor M 1 at the drain.

Transistor M 1 is provided with a gate terminal Vc 1 connected to control circuit 400 and has its source connected to a first fixed potential (a ground potential). Transistor M 2 is provided with a gate terminal Vc 2 connected to control circuit 400 and has its source connected to the first fixed potential (the ground potential).

Transistor M 3 has its gate connected to its drain. Transistor M 4 has its gate connected to its drain. Transistor M 6 has its gate connected to a first input terminal IN 1 . Transistor M 5 has its gate connected to a second input terminal IN 2 .

Resistance Z1 has one end connected to a second fixed potential Vdd and the other end to a first output terminal OUT 1 . Resistance Z2 has one end connected to the second fixed potential Vdd and the other end to a second output terminal OUT 2 .

Input terminals IN 1 and IN 2 have potentials Vin− and Vin+, respectively, and output terminals OUT 1 and OUT 2 have potentials Vout+ and Vout−, respectively, and transistors M 1 and M 2 pass currents I1 and I2, respectively, for the sake of illustration.

FIG. 6 shows a circuit equivalent to the amplification circuit. In the figure, gm1 represents transconductance of transistors M 5 and M 6 , gm2 represents transconductance of transistors M 3 and M 4 , rd1 represents drain resistance of transistors M 5 and M 6 , rd2 represents drain resistance of transistors M 3 and M 4 , and Z represents resistance of load resistances Z1 and Z2. From this figure, the amplification circuit has a gain gain, as represented by the following equation: gain =  ( ( Vout + - Vout - ) ( Vin + - Vin - ) )  

   = g     m     1 · ( rd     1 // rd     2 // 1 gm     2 // Z ) , ( A1 )

wherein // indicates an operation performed to calculate combined resistance of parallel connection. If rd1, rd2>>1/gm2, Z then gain is approximated, as follows: gain ≅ gm     1 · ( 1 gm     2 // Z ) 

   = gm     1 · ( Z gm     2 Z + 1 gm     2 ) 

   = gm     1 gm     2 · 1 1 Z · gm     2 + 1 . ( A2 )

If μ n represents an average surface mobility, Cox represents a gate capacitance per unit area, (W/L) 1 represents a channel width/a channel length of transistors M 5 and M 6 , and (W/L) 2 represents a channel width/a channel length of transistors M 3 and M 4 , then gm1 and gm2 are represented by the following equations: gm     1 = UnCox  ( W L ) 1 · I     1 ( A3 ) gm     2 = UnCox  ( W L ) 2 · I     2 . ( A4 )

By substituting expressions A3 and A4 into expression A2, the following expression: gain ≅ UnCox  ( W L ) 1 · I     1 UnCox  ( W L ) 2 · I     2 × 1 1 Z  UnCox  ( W L ) 2 · I     2 ( A5 )

is obtained.

From expression A5, if Z is sufficiently large, then an expression:

gain ∝(I1/I2) 0.5   (A6)

is provided and gain is proportional to a square root of a ratio of current I1 to current I2.

Control circuit 400 is configured, as described hereinafter. Control circuit 400 includes p-channel MOS transistors M 21 and M 22 , n-channel MOS transistors M 11 and M 12 , and a constant current source Ibias1. Herein, transistors M 11 and M 12 are identical in characteristics, and so are transistors M 21 and M 22 .

Constant current source Ibias1 outputs a constant current Ibs1.

Transistors M 21 has its source connected to constant current source Ibias1, its drain connected to transistor M 11 at the drain, and its gate receiving a control voltage Vcon1.

Transistor M 22 has its source connected to constant current source Ibias1, its drain connected to transistor M 12 at the drain, and its gate receiving a control voltage Vcon2.

Transistor M 11 has its source connected to a first fixed potential (a ground potential), its drain connected to its gate and transistor M 21 at the drain, and gate terminal Vc 1 connected to gate terminal Vc 1 of transistor M 1 of amplification circuit 100 .

Transistor M 12 has its source connected to the first fixed potential (the ground potential), its drain to its gate and transistor M 22 at the drain, and gate terminal Vc 2 to gate terminal Vc 2 of transistor M 2 of amplification circuit 100 .

Constant current source Ibias1 has one end connected to a second fixed potential Vdd and the other end to transistors M 21 and M 22 at their respective sources.

Control circuit 400 operates, as described hereinafter. Transistors M 21 and M 22 are provided with a gain constant K and a threshold voltage Vth for the sake of illustration. Transistors M 21 and M 22 pass currents Id1 and Id2, respectively, and their respective gate-source voltages are represented as Vgs1 and Vgs2, respectively, for the sake of illustration. Currents Id1 and Id2 are represented by the following equations:

Ibs 1= Id 1+ Id 2   (A7)

Id 1= K× ( Vgs 1 −Vth ) 2   (A8)

Id 2= K× ( Vgs 2 −Vth ) 2   (A9).

Herein, if a point S has a potential Vs then the following equations:

Vgs 1 =Vcon 1 −Vs   (A10)

Vgs 2 =Vcon 2 −Vs   (A11)

are established.

Herein, if

Vcon=Vcon 2 −Vcon 1   (A12)

then from expressions A7-A12 the following expressions:

{square root over (K)} Vcon={square root over (Ibs 1− Id 1)}− {square root over (Id1)}   (A13)

={square root over (Id2)} −Ibs 1− {square root over (Id2)}   (A14)

are obtained.

Expressions A13 and A14 are transformed to obtain the following two expressions: Id     1 = 1 2  [ Ibs     1 + 2  Ibs     1 · K - ( K · Vcon ) 2 · Vcon ] ( A15 ) Id     2 = 1 2  [ Ibs     1 - 2  Ibs     1 · K - ( K · Vcon ) 2 · Vcon ] . ( A16 )

FIG. 7 represents a relationship between Vcon, and Id1 and Id2. As shown in the figure, in a vicinity of Vcon=0, Id1 is directly proportional to Vcon and Id2 is directly proportional to −Vcon.

If A = 1 2  Ibs     1 ( A17 ) B = 1 2  2  Ibs     1 · K - ( K · Vcon ) 2 ( A18 )

then from expressions A15-A18 currents Id1 and Id2 are represented by the following equations:

Id 1= A+B×Vcon   (A19)

Id 2= A−B×Vcon   (A20).

Current Id1 also flows through transistor M 11 . Since transistors M 11 and M 1 configure a current mirror circuit, current Id1 also flows through transistor M 1 . Therefore I1=Id1. Furthermore, current Id2 also flows through transistor M 12 . Since transistors M 12 and M 2 configure a current mirror circuit, current Id2 also flows through transistor M 2 . Therefore I2=Id2. C = B A = 2  Ibs     1 · K - ( K · Vcon ) 2 Ibs     1 ( A21 )

is provided and from expressions A6 and A19-A21 gain is represented by the following equation: gain ∝ ( I     1 I     2 ) 0.5 = ( Id     1 Id     2 ) 0.5 

   = ( A + B · Vcon A - B · Vcon ) 0.5 

   = ( 1 + C · Vcon 1 - C · Vcon ) 0.5 . ( A22 )

In general, an exponential function is approximated by the following expression:

exp(2 nx )≈{(1 +x )/(1 −x )} n   (A23).

If

Vcon′=C×Vcon   (A24)

and approximation A23 for n=0.5 is applied to expression A22, then

gain ∝ exp(Vcon′)   (A25).

This indicates that the gain is proportional to an exponential function of a control voltage. If the gain is represented in dB then it exhibits a linear in dB characteristic relative the control voltage. A variable gain amplifier allowing a gain to have a linear in dB characteristic relative to a control voltage is referred to as a linear gain amplifier.

Approximation A23 for n=0.5, however, is established only in a small range. More specifically, for Y1={(1+x)/(1−x)} 0.5 and Y2=exp(x), Y1 that allows an approximation Y1≈Y2 to be established has a small range. In other words, for the above described, conventional variable gain amplifier, a gain exhibits a linear in dB characteristic relative to a control voltage in a small range.

The present invention contemplates a variable gain amplifier allowing a gain to exhibit a linear in dB characteristic relative to a control voltage over a range wider than conventional.

The present invention in one aspect provides a variable gain amplifier including: an amplification circuit including first and second MOS transistors identical in characteristics and having respective sources connected to a first fixed potential, the amplification circuit having a differential gain proportional to a square root of a ratio between a current flowing through the first MOS transistor and a current flowing through the second MOS transistor; and a control circuit applying a potential corresponding to a constant voltage plus a control voltage to a gate of the first MOS transistor and a potential corresponding to the constant voltage minus the control voltage to a gate of the second MOS transistor.

As such, when the constant voltage and the control voltage are represented as Vb and Vcon, respectively, the first MOS transistor has its gate receiving a potential Vb+Vcon and the second MOS transistor has its gate-receiving a potential Vb−Vcon. As such, the first MOS transistor passes current I1 represented in the order of (Vb+Vcon) 2 and the second MOS transistor passes current I2 represented in the order of (Vb−Vcon) 2 so that a gain can exhibit A linear in dB characteristic for the control voltage over a range wider than conventional.

The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings.

In the drawings:

FIG. 1 shows a configuration of a variable gain amplifier of an embodiment of the present invention;

FIG. 2 represents a range of a linear in dB in each of a variable gain amplifier of an embodiment of the present invention and a conventional variable gain amplifier;

FIG. 3 shows a configuration of a variable gain amplifier of an embodiment of the present invention;

FIG. 4 shows a configuration of a constant current circuit used as a constant current source Ibias2 serving as a component of a control circuit;

FIG. 5 shows a configuration of a conventional variable gain amplifier;

FIG. 6 shows a circuit equivalent to amplification circuit 100 ; and

FIG. 7 represents a relationship between Vcon, and Id1 and Id2.

Hereinafter the present invention in embodiments will be described with reference to the drawings.

First Embodiment

The present embodiment relates to a variable gain amplifier allowing a gain to exhibit a linear in dB characteristic relative to a control voltage over a range wider than conventional.

Configuration

With reference to FIG. 1, the present embodiment provides a variable gain-amplifier configured of an amplification circuit 100 and a control circuit 200 . Amplification circuit 100 will not be described as it is identical to the conventional amplification circuit shown in FIG. 5 .

Control circuit 200 includes n-channel MOS transistors M 3 -M 34 (seventh to tenth MOS transistors, respectively), p-channel MOS transistors M 41 and M 42 , and a constant current source Ibias2. Herein, transistors M 31 and M 33 are identical in characteristics, and so are transistors M 32 and M 34 , and transistors M 41 and M 42 .

Constant current source Ibias2 outputs a constant current Ibs2.

Transistor M 31 has its source connected to a first fixed potential (a ground potential) and its drain connected to transistor M 33 at the source. Transistor M 31 is provided with a drain terminal Vc 2 connected to a gate terminal Vc 2 of transistor M 2 of amplification circuit 100 . Furthermore, transistor M 31 is provided with a gate terminal Vc 1 connected to a gate terminal Vc 1 of transistor M 1 of amplification circuit 100 . Gate terminal Vc 1 receives a gate voltage Vg32 of transistor M 32 plus a control voltage Vcon.

Transistor M 33 has its source connected to transistor M 31 at the drain, its drain connected to a second fixed potential Vdd, and its gate connected to transistor M 34 at the gate. Transistors M 31 and M 33 configures a level shift circuit.

Transistor M 32 has its source connected to a first fixed potential (a ground potential), its drain connected to transistor M 34 at the source, and its gate connected to its drain.

Transistor M 34 has its source connected to transistor M 32 at the drain, its drain connected to its gate and transistor M 41 at the drain, and its gate connected to transistor M 33 at the gate.

Transistor M 41 has its source connected to the second fixed potential Vdd, its drain connected to transistor M 34 at the drain, and its gate connected to transistor M 42 at the gate.

Transistor M 42 has its source connected to the second fixed potential Vdd, its drain connected to its gate and constant current source Ibias2, and its gate connected to transistor M 41 at the gate. Transistors M 41 and M 42 configures a current mirror circuit.

Operation

Control circuit 200 operates, as will be described hereinafter. All transistors operate in a saturation range for the sake of illustration.

Transistors M 41 and M 42 configure a current mirror circuit. Since transistors M 41 and M 42 are identical in characteristics, they have their respective drains both passing a current Id represented by Ibs2. Accordingly, transistors M 34 and M 32 also have their respective drains passing current Id represented by Ibs2.

Since transistors M 32 and M 34 are identical in characteristics, their gain constant and threshold are represented as K and V, respectively. Gate-source voltages Vgs 32 and Vgs 34 of transistors M 32 and M 34 , respectively, are represented as follows: Vgs     32 = Vgs     34 = Ibs     2 K + Vth ( B1 )

Herein, if Vb = Ibs     2 K + Vth ( B2 )

then the following equation:

Vgs32=Vgs34=Vb   (B3)

is obtained.

Since transistor M 32 has its source grounded, transistor M 32 has a gate voltage Vg32 based on expression B3, as follows:

Vg32=Vgs32=Vb   (B4).

Furthermore, since the transistor M 32 gate and the transistor M 34 source are connected together, transistor M 34 has a gate voltage Vg34 based on expressions B3 and B4, as follows:

Vg 34 =Vg 32 +Vgs 34=2 Vb   (B5).

Transistors M 31 and M 33 configure a level shift circuit. Since transistors M 31 and M 33 are identical in characteristics, their respective gate-source voltages Vgs31 and Vgs33 are represented as follows:

Vgs31=Vgs33   (B6).

Furthermore, since transistor M 31 has its source grounded, the following expression:

Vg31=Vgs31   (B7)

is established.

From expressions B6 and B7, the following expression:

Vc 2 = Vg 33 −Vgs 33 =Vg 33 −Vg 3   (B8)

is obtained.

Since the transistor M 33 gate is connected to the transistor M 34 gate, transistor M 33 has a gate voltage Vg33 based on expression B5, as follows:

Vg33=Vg34=2Vb   (B9).

When control voltage Vcon is applied between the transistor M 31 gate and the transistor M 32 gate, from expression B4 the following equation:

Vc 1 = Vg 31 =Vg 32 +Vcon=Vb+Vcon   (B10)

is obtained.

From expressions B8-B10, the following equation:

Vc 2=2 Vb −( Vb+Vcon )= Vb−Vcon   (B11)

is obtained.

In amplification circuit 100 transistor M 1 passes current I1 based on expression B10, as represented by:

I 1= K ( Vgs 1 −Vth ) 2 =K ( Vc 1 − Vth ) 2 =K ( Vb+Vcon−Vth ) 2   (B12).

Similarly, in amplification circuit 100 transistor M 2 passes current I2 based on expression B11, as represented by:

I 2= K ( Vgs 2 −Vth ) 2 =K ( Vc 2 − Vth ) 2 =K ( Vb−Vcon−Vth ) 2   (B13).

From expressions A6, B12 and B13, gain is expressed as follows: gain ∝  ( I1 I2 ) 0.5 =  { K  ( Vb + Vcon - Vth ) 2 K  ( Vb - Vcon - Vth ) 2 } 0.5 =  Vb + Vcon - Vth Vb - Vcon - Vth =  1 + Vcon Vb - Vth 1 - Vcon Vb - Vth . ( B14 )

If

Vcon′=Vcon /( Vb−Vth )   (B15)

and n=1, and for expression B14 approximation A23 is used, then

gain ∝ exp(2Vcon′)   (B16).

While for a conventional variable gain amplifier gain is approximated by approximation A23 for n=0.5, for the variable gain amplifier of the present embodiment gain is approximated by approximation A23 for n=1.

The variable gain amplifier of the present embodiment and the conventional variable gain amplifier each have a gain exhibiting a linear in dB relative to a control voltage over a range, as will now be described with reference to FIG. 2 . In the figure Y1={(1+x)/(1−x)} 0.5 , Y2=exp(x), Y3={(1+x)/(1−x)} 1 and Y4=exp(2x), and Y1-Y4 are represented in dB.

For the conventional variable gain amplifier, Y1 is approximated by Y2, and the range of x allowing 20×logY1 and 20×logY2 to have a difference of no more than ±1 dB (i.e., a range allowing approximation) is −0.64<×<0.64, and the range of 20×logY1 that corresponds to this range of x is −6.5 dB to 6.5 dB.

In contrast, for the variable gain amplifier of the present embodiment, Y3 is approximated by Y4, and the range of x allowing 20×logY1 and 20×logY2 to have the difference of no more than ±1 dB (i.e., a range allowing approximation) is −0.52<×<0.52, and the range of 20×logY3 that corresponds to this range of x is −10 dB to 10 dB.

In other words, for the conventional variable gain amplifier, a linear in dB characteristic is obtained only over the range of −6.5 dB to 6.5dB, whereas for the variable gain amplifier of the present embodiment, a linear in dB characteristic is obtained over a range wider than conventional, i.e., −10 dB to 10 dB.

Thus in the variable gain amplifier of the present embodiment transistors M 1 and M 2 have their respective gates receiving potentials Vb+Vcon and Vb−Vcon, respectively, to allow transistors M 1 and M 2 to pass currents I1 and I2 represented in orders of (Vb+Vcon) 2 and (Vb−Vcon) 2 , respectively, so that in expression A23 an approximation for n=1 can be established and a gain can exhibit a linear in dB characteristic relative to a control voltage over a range wider than conventional.

Second Embodiment

The present embodiment relates to a variable gain amplifier that allows a gain to exhibit a linear in dB characteristic relative to a control voltage over a range wider than conventional.

Configuration With reference to FIG. 3, the present embodiment provides a variable gain amplifier configured of amplification circuit 100 and a control circuit 300 . Amplification circuit 100 will not be described as it is identical to the conventional amplification circuit shown in FIG. 5 and the amplification circuit shown in FIG. 1 .

Control circuit 300 includes p-channel MOS transistors M 61 and M 62 , n-channel MOS transistors M 51 -M 58 (11th to 18th MOS transistors, respectively), and a constant current source Ibias3.

Transistors M 51 and M 52 are identical in characteristics, and so are transistors 53 and M 54 , transistors M 55 and M 56 , transistors M 57 and M 58 , and transistors M 61 and M 62 .

Constant current source Ibias3 outputs a constant current Ibs3.

Transistor M 51 has its source connected to a first fixed potential (a ground potential), its drain connected to transistor M 52 at the source, and its gate connected to transistor M 53 at the drain. Transistor M 51 is provided with a drain terminal Vc 2 connected to gate terminal Vc 2 of transistor M 2 of amplification circuit 100 . Furthermore transistor M 51 is provided with a gate terminal Vc 1 connected to gate terminal Vc 1 of transistor M 1 of amplification circuit 100 .

Transistor M 52 has its source connected to transistor M 51 at the drain, its drain to a second fixed potential Vdd, and its gate to transistor M 58 at the gate. Transistors M 51 and M 52 configure a level shift circuit.

Transistor 53 has its source connected to a first fixed potential (a ground potential), its drain to transistor 54 at the source and transistor M 51 at the gate, and its gate connected to transistor M 55 at the drain.

Transistor M 54 has its source connected to transistor M 53 at the drain, its drain to the second fixed potential Vdd, and its gate receiving a control voltage Vcon2. Transistors M 53 and M 54 configure a level shift circuit.

Transistor M 55 has its source connected to the first fixed potential (a ground potential), its drain to transistor M 56 at the source and transistor M 53 at the gate, and its gate to transistor M 57 at the drain.

Transistor M 56 has its source connected to transistor M 55 at the drain and transistor M 53 at the gate, its drain to the second fixed potential Vdd, and its gate receiving a control voltage Vcon1. Transistors M 55 and M 56 configure a level shift circuit.

Transistor M 57 has its source connected to the first fixed potential (a ground potential), its drain to transistor M 58 at the source and its gate, and its gate to transistor M 55 at the gate.

Transistor M 58 has its source connected to transistor M 57 at the drain, its drain to transistor M 61 at the drain and its gate, and its gate to transistor M 52 at the gate.

Transistor M 61 has its source connected to the second fixed potential Vdd, its drain to transistor M 58 at the drain, and its gate to transistor M 62 at the gate.

Transistor M 62 has its source connected to the second fixed potential Vdd, its drain to its gate and constant current source Ibias3, and its gate to transistor M 61 at the gate. Transistors M 61 and M 62 configure a current mirror circuit.

Operation

Control circuit 300 operates as described hereinafter. All transistors operate in a saturation range for the sake of illustration.

Transistors M 61 and M 62 configure a current mirror circuit. Since transistors M 61 and M 62 are identical in characteristics, they have their respective drains both passing a current Id represented by Ibs3. Accordingly, transistors M 58 and M 57 also have their respective drains passing current Id represented by Ibs3.

Since transistors M 57 and M 58 are identical in characteristics, their gain constant and threshold are represented as K and V, respectively. Gate-source voltages Vgs 57 and Vgs 58 of transistors M 57 and M 58 , respectively, are represented as follows: Vgs57 = Vgs58 = Ibs3 K + Vth ( C1 ) Herein , if   Vb = Ibs3 K + Vth ( C2 )

then

Vgs57=Vgs58=Vb   (C3).

Since transistor M 57 has its source grounded, transistor M 57 has a gate voltage Vg57 based on expression C3, as follows:

Vg57=Vgs57=Vb   (C4).

Furthermore, since the transistor M 57 gate and the transistor M 58 source are connected together, transistor M 58 has a gate voltage Vg58 based on expressions C3 and C4, as follows:

Vg 58 =Vg 57 +Vgs 57=2 Vb   (C5).

Transistors M 55 and M 56 configure a level shift circuit. Since transistors M 55 and M 56 are identical in characteristics, their respective gate-source voltages Vgs55 and Vgs56 are represented as follows:

Vgs55=Vgs56   (C6).

Furthermore, since transistor M 55 has its source grounded, the following expression:

Vg55=Vgs55   (C7).

is established.

Furthermore, since transistors M 55 and M 57 have their respective gates connected together, the following expression:

Vg55=Vg57=Vb   (C8).

is established.

If transistor M 55 has a drain voltage Vd55, then from expressions C6 and C7 the following expression:

Vd 55 =Vg 56 −Vgs 56 =Vg 56 −Vg 55   (C9)

is obtained.

Furthermore, transistors M 53 and M 54 configure a level shift circuit. Since transistors M 53 and M 54 are identical in characteristics, their respective gate-source voltages Vgs53 and Vgs54 are represented as follows:

Vgs53=Vgs54   (C10).

Furthermore, since transistor M 53 has its source grounded, the following expression:

Vg53=Vgs53   (C11)

is established.

Since the transistor M 53 drain is connected to transistor M 54 source, if transistor M 53 has a drain voltage Vd53 then the following expression:

Vd 53 =Vg 54 −Vgs 54   (C12)

is established.

From expressions C10-C12 the following expression:

Vd 53 =Vg 54 −Vg 53   (C13)

is obtained.

Furthermore, since the transistor M 53 gate and the transistor M 55 drain are connected together, the following expression:

Vg53=Vd55   (C14)

is established.

From expressions C9-C11, C13 and C14 the following expression: Vd53 =  Vg54 - Vgs53 =  Vg54 - Vg53 =  Vg54 - Vd55 =  Vg54 - ( Vg56 - Vg55 ) =  Vg55 + ( Vg54 - Vg56 ) ( C15 )

is obtained.

Herein if Vd53=Vc 1 , Vg54=Vcon2, and Vg56=Vcon1, then from expression C8 the following expression:

Vc 1 = Vb +( Vcon 2 −Vcon 1)   (C16)

is obtained.

Transistors M 51 and M 52 configure a level shift circuit. Since transistors M 51 and M 52 are identical in characteristics, their respective gate-source voltages Vgs51 and Vgs52 are represented as follows:

Vgs52=Vgs51   (C17).

Since transistors M 52 and M 58 have their respective gates connected together, from expression C3 the following expression:

Vg52=Vg58=2 Vb   (C18)

is established. Furthermore, since transistor M 51 has its source grounded, the following expression:

Vg51=Vgs51   (C19)

is established. Since the transistor M 51 drain and the transistor M 52 source are connected together, the following expression:

Vd 51 =Vg 52 −Vgs 52   (C20)

is established.

From expressions C17, C19 and C20 the following expression:

Vd 51 =Vg 52 −Vg 51   (C21)

is obtained. Herein, if Vd51=Vc 2 , and Vg51=Vc 1 , then from expressions C16, C18 and C21 the following expression: Vc2  = Vg52 - Vc1  = 2  Vb - Vc1  = 2  Vb - { V     b + ( Vcon     2 - Vcon     1 ) }  = V     b - ( Vcon     2 - Vcon1 ) ( C     22 )

is obtained.

Herein if

Vcon=Vcon 2 −Vcon 1   (C23)

then the following expressions:

Vc 1 = Vb+Vcon   (C24)

Vc 2 = Vb−Vcon   (C25)

are obtained.

In amplification circuit 100 transistor M 1 passes current I1 based on expression C24, as represented by:

I 1= K ( Vgs 1 −Vth ) 2 =K ( Vc 1 − Vth ) 2 =K ( Vb+Vcon−Vth ) 2   (C26).

Similarly in amplification circuit 100 transistor M 2 passes current I2 based on expression C25, as represented by:

I 2= K ( Vgs 2 −Vth ) 2 =K ( Vc 2 − Vth ) 2 =K ( Vb−Vcon−Vth ) 2   (C27).

From expression A6, C26 and C27, gain is represented by the following expression: gain ∝  ( I1 I2 ) 0.5 =  { K  ( Vb + Vcon - Vth ) 2 K  ( Vb - Vcon - Vth ) 2 } 0.5 =  Vb + Vcon - Vth Vb - Vcon - Vth =  1 + Vcon Vb - Vth 1 - Vcon Vb - Vth . ( C28 )

If

Vcon′=Vcon /( Vb−Vth )   (C29)

and to expression C28 approximation A23 for n=1 is applied then:

gain ∝ exp(2Vcon′)   (C30).

As such, as well as for the variable gain amplifier of the first embodiment, for that of the present embodiment gain is approximated by approximation A23 for n=1.

Thus in the variable gain amplifier of the present embodiment transistors M 1 and M 2 have their respective gates receiving potentials Vb+Vcon and Vb−Vcon, respectively, to allow transistors M 1 and M 2 to pass currents I1 and I2 represented in orders of (Vb+Vcon) 2 and (Vb−Vcon) 2 , respectively, so that in expression A23 an approximation for n=1 can be established and a gain can exhibit a linear in dB characteristic relative to a control voltage over a range wider than conventional.

Furthermore in the present embodiment the variable gain amplifier allows a gain to be controlled by a differential value Vcon of two control Vcon2 and Vcon1. As such, if the variable gain amplifier is configured of MOS transistors having characteristics (e.g., threshold voltage, size and the like) more or less varying, adjusting Vcon2 and Vcon1 in absolute value while maintaining differential value Vcon allows the variation to be absorbed.

Third Embodiment

If in the first embodiment, expression B2 is substituted into expression B14, then gain is expressed by: gain ∝ 1 + Vcon Ibs2 K 1 - Vcon Ibs2 K . ( D1 )

Herein, in general, an MOS transistor's gain constant varies in the order of the −3/2 power of temperature. Accordingly, when temperature varies, in expression D1 the transistors M 31 and M 32 gain constant K also varies and accordingly the variable gain amplifier's gain varies.

As such, if Ibs2 is proportional to a gain constant K′ of any MOS transistor, which may be other than transistors M 32 and M 34 , then K′/K allows an item related to temperature variation to be cancelled and if temperature varies the variable gain amplifier's gain can be maintained to be constant. The present embodiment relates to a variable gain amplifier including a constant current circuit outputting Ibs2 in proportion to gain constant K′ of an MOS transistor.

Configuration

The present embodiment provides a variable gain amplifier including an amplification circuit and a control circuit identical to those shown in FIG. 1 . FIG. 4 shows a constant current circuit used as constant current source Ibias2 serving as a component of the control circuit shown in FIG. 1 . The constant current circuit includes p-channel MOS transistors M 81 and M 82 , n-channel MOS transistors M 71 -M 74 (19th to 22nd MOS transistors, respectively), voltage sources Vps1 and Vps2, and a constant current source Ibias4. Transistors M 81 and 82 are identical in characteristics, and so are transistors M 71 -M 74 .

Voltage sources Vps1 and Vps2 supply a voltage Vx. Constant current source Ibias4 outputs a constant current Ibs4.

Transistor M 81 has its source connected to a second fixed potential Vdd, its drain to transistors M 71 and M 73 at the drains, respectively, and its gate to transistor M 82 at the gate.

Transistor M 82 has its source connected to the second fixed potential Vdd, its drain to its gate and transistors M 72 and M 74 at the drains, respectively, and its gate to transistor M 82 at the gate. Transistors M 81 and M 82 configure a current mirror circuit.

Transistor M 71 has its source connected to constant current source Ibias4, its drain to transistors M 81 and M 73 at the drains, respectively, and its gate to a fourth fixed potential Vb.

Transistor M 73 has its source connected to constant current source Ibias4, its drain to transistors M 81 and M 71 at the drains, respectively, and its gate to a third fixed potential Va via voltage source Vps1.

Transistor M 72 has its source connected to constant current source Ibias4, its drain to transistors M 82 and M 74 at the drains, respectively, and its gate to the fourth fixed potential Vb via voltage source Vps2.

Transistor M 74 has its source connected to constant current source Ibias4, its drain to transistors M 82 and M 72 at the drains, respectively, and its gate to the third fixed potential Va at the gate.

Constant current source Ibias4 has one end connected to a first fixed potential (a ground potential) and the other end to transistors M 71 -M 74 at the sources.

Operation

The constant current circuit operates, as described hereinafter. All transistors operate in a saturation range for the sake of illustration. Since transistors M 71 -M 74 are identical in characteristics, their gain constant and threshold voltage are represented by K′ and Vth, respectively.

Transistors M 71 -M 74 have their respective drains passing currents Id71-Id74, respectively, for the sake of illustration. If their common source terminal represented as a point S has a potential Vs. then the following four expressions:

Id 71= K′ ( Vb−Vs−Vth ) 2   (D2)

Id 72= K′ ( Vb−Vx−Vs−Vth ) 2   (D3)

Id 73= K′ ( Va−Vx−Vs−Vth ) 2   (D4)

Id 74= K′ ( Va−Vs−Vth ) 2   (D5)

are established.

Furthermore, transistors M 81 and M 82 configure a current mirror circuit. Since transistors M 81 and M 82 are identical in characteristics, an output terminal OUT outputs a current Ibs2, as represented by the following equation:

Ibs 2=( Id 72+ Id 74)−( Id 71+ Id 73)   (D6).

By substituting expressions D2-D5 into expression D6, the following equation:

Ibs 2=2 K′×Vx ×( Va−Vb )   (D7)

is obtained.

Output current Ibs2 proportional to gain constant K′ is supplied to the drain of transistor M 42 of FIG. 1 .

Thus in the present embodiment the variable gain amplifier includes a constant current circuit outputting current Ibs2 proportional to gain constant K′ of an MOS transistor. As such, even if temperature varies, a gain can be maintained to be constant.

Variation

The present invention is not limited to the above described embodiments and of course encompasses the following variations:

(1) The circuits described in the first and third embodiments can be operated, similarly as described above, if they have the p-channel MOS transistors replaced with n-channel MOS transistors and the n-channel MOS transistors replaced with p-channel MOS transistors;

(2) In the first embodiment, transistor M 34 has its drain connected to a constant current circuit configured by a current mirror circuit formed of transistors M 41 and M 42 and constant current source Ibias2 (i.e., a circuit outputting constant current Ibs2) to supply transistor M 41 with a constant current. However, the present invention is not limited thereto. For example, transistor M 41 may have its drain directly connected to constant current source Ibias2. Furthermore, as described in the embodiment, transistors M 41 and M 42 configuring a current mirror circuit are identical in characteristics and transistor M 41 passes a current set to be equal to the amount of current Ibs2 supplied from constant current source Ibias2. However, the present invention is not limited thereto. Any source that supplies a constant current can be used. For example, transistors M 41 and M 42 may be different in characteristics and transistor M 34 may pass a current proportional to Ibs2;

(3) In the second embodiment, transistor M 58 has its drain connected to a constant current circuit configured by a current mirror circuit formed of transistors M 61 and M 62 and constant current source Ibias3 (i.e., a circuit outputting constant current Ibs3) to supply transistor M 58 with a constant current. However, the present invention is not limited thereto. For example, transistor M 58 may have its drain directly connected to constant current source Ibias3. Furthermore, as described in the embodiment, transistors M 61 and M 62 configuring a current mirror circuit are identical in characteristics and transistor M 58 passes a current set to be equal to the amount of current Ibs3 supplied from constant current source Ibias3. However, the present invention is not limited thereto. Any source that supplies a constant current can be used. For example, transistors M 61 and M 62 may be different in characteristics and transistor M 58 may pass a current proportional to Ibs3;

(4) The constant current circuit of the third embodiment may be used as constant current source Ibias3 of the second embodiment. In this variation, an output current proportional to gain constant K′ of an MOS transistor is supplied to the drain of transistor M 62 shown in FIG. 3; and

(5) The variable gain amplifier may include an amplification circuit other than those described in the first and second embodiments and the conventional example. The amplification circuit may have any configurations except that as well as those having been described, it includes transistors M 1 and M 2 and has a gain proportional to a square root of a ratio between current I1 flowing through transistor M 1 and current I2 flowing through transistor M 2 .

Although the present invention has been described and illustrated in detail, it is clearly understood that the same is by way of illustration and example only and is not to be taken by way of limitation, the spirit and scope of the present invention being limited only by the terms of the appended claims.