32
Why Use Differential Amplifiers?
■
Single-ended detection using a variable resistor
1. need to consider DC level ... sets VBIAS
2. “junk” pickup (antenna) on possibly long interconnection -->
appears at the amplifier input
VDD
iSUP
vjunk
R
VBIAS
vO
- +
R(P)
R(P) represents a pressure-sensitive resistor
R(P) = R + ∆R where ∆R ∝ P
another example: a temperature-sensitive resistor = “thermistor”
EECS 105 Fall 1998
Lecture 32
Differential Interface Circuit
■
■
Use Wheatstone bridge: voltage on one side goes up with pressure; voltage on
the other side goes down
R +(P) = R + ∆R and R -(P) = R + ∆R
Use a differential amplifier as the input stage
VDD
RD
R-(P)
R+(P)
- +
R+(P)
■
R-(P)
RD
+ vo _
vjunk
- +
vjunk
IBIAS
Interfering voltage vjunk is common to both inputs of the differential pair:

 

R + ∆R
R – ∆R
v ID =  V DD  -------------------------------------- + v junk  –  V DD  ----------------------------------------- + v junk 
 R – ∆R + R – ∆ R
 R + ∆R + R – ∆R

 

■
∆R
2∆R
v id = V DD  ----------- = V DD  -------
 R
 2R 
Note that vjunk is common to both inputs and is rejected by the CMRR of the
amplifier
EECS 105 Fall 1998
Lecture 32
Differential Amplifier with Single-Ended Outputs
■
An output voltage referenced to ground is important in some applications
Simple approach: take the output from one side
V+
RC
RC
+
vo
−
Q1
vi 1
Q2
+
−
+
−
IBIAS
vi 2
rob
V−
Purely differential input voltage --> vo2 = -vod/2 = -(1/2)adm vid
gm RC
vo
1
------- = –  --- ( – g m R C ) = -------------2
v
2
id
Sign change (since vπ2 = - vid/2) and a loss of 50% of gain
EECS 105 Fall 1998
Lecture 32
Differential Amplifier with Current Supplies
■
Boost gain by using current supplies adjusted to IBIAS/2 instead of RC
V+
IBIAS
IBIAS
2
2
M1
vi1
+
vo1
+
vo2
−
−
M2
+
−
+
−
vi 2
IBIAS
V−
adm = -gm(ro||roc) for this differential amplifier
Drawbacks:
Bias stability is not possible without a feedback circuit
Taking the output from one side still reduces the gain by 50%
EECS 105 Fall 1998
Lecture 32
Differential Amplifier with Current Mirror Supply
■
By substituting a current mirror (diode voltage source biasing a current source
transistor), this amplifier has a stable bias
V+
IBIAS
2
+gmvgs1
M3
vi1
+
−
M1
vgs1
2
iD 2 =
I
iD1 = BIAS +gmvgs1
2
+
IBIAS
M4
IBIAS
M2
−
−
IBIAS
vgs 2
2
+ gmvgs1
io = iD2 − iD1 = gm(vgs 2 − vgs1)
+ gmvgs2
+
vo
−
+
+
−
vi 2
rob
V−
The output node should be held at a constant DC potential
VOUT = V+ - VSG3
so that the amplifier is balanced and the output is a small-signal short-circuit
■
Note that this amplifier is not symmetrical and that half circuits do not apply
EECS 105 Fall 1998
Lecture 32
Short-Circuit Transconductance Gmd
■
Approximate circuit analysis:
I BIAS
i D1 = I D1 + g m1 v gs1 = ------------- + g m v gs1
2
I BIAS
i D2 = I D2 + g m2 v gs2 = ------------- + g m v gs2
2
Current mirror forces the drain current -iD4 = -iD3 = iD1
Kirchhoff’s current law at the output states that
i O = i D2 – ( – i D4 ) = i D2 – i D1
I BIAS
I BIAS
i O =  ------------- + g m v gs2 –  ------------- + g m v gs1 = g m ( v gs2 – v gs1 )
 2
  2

Kirchhoff’s voltage law at the input states that vgs2 - vgs1 = vi2 - vi1 = -vid
i o = g m ( – v id ) -->
■
io
G md = ------- = – g m
v id
No factor of two in converting differential input into a single-ended current!
EECS 105 Fall 1998
Lecture 32
Output Resistance Rod
■
The current-mirror circuit is not symmetrical, so the procedure must be applied
to the entire amplifier
ro3
gm3vsg3
+
+
vsg3
vsg4
−
−
io3
io4
io1
io2
+
vgs1
ro4
gm4vsg4
it
+
−
vt
+
gm1vgs1
ro1
ro2
−
gm2vgs2
vx
vgs2
−
rob
■
Complicated analysis (see Section 11.5), but a simple result
R od = r o2 r o4
EECS 105 Fall 1998
Lecture 32
Two-Port Differential Model:
Current-Mirror Supply
■
The output port is referenced to ground, in contrast to the earlier model of the
symmetrical amplifier with vo = vod
Rod
+
vd
+
Gmdvd
−
Rod
vd
+
−
avdvd
−
(a)
(b)
EECS 105 Fall 1998
Lecture 32
Input Common-Mode Voltage Range
■
The range of DC common-mode inputs over which the differential amplifier can
function is an important practical specification (see op amp spec. sheets)
V+
RC
RC
VIC
+
V
+ IN
−
−
1
+
VO1
+
VO2
−
−
VX
2
+
VIN +
VIC
−
−
IBIAS
3
V−
Upper limit to VIC
devices 1 and 2 leave their constant-current regions
Lower limit to VIC
bias current device 3 leaves its constant-current region
EECS 105 Fall 1998
Lecture 32
All-Bipolar Differential Amplifier VIC Range
■
Maximum common-mode input voltage:
VO1 = V+ - (IBIAS/2)RC
Q1 enters saturation when VBC1 = VBE1 - VCE(sat)1 = 0.7 V - 0.1 V = 0.6 V
I BIAS
+
V IC(max) = V O1 + 0.6 V = V –  ------------- R C + 0.6 V
 2 
■
Minimum common-mode input voltage:
VX = VIC - VBE1 = VIC - 0.7 V
Q3 enters saturation when VX - V - = VCE(sat)3 = 0.1 V
-
-
V IC(min) = V X + V BE1 = V + V CE(sat)3 + V BE1 = V + 0.8 V
EECS 105 Fall 1998
Lecture 32