differential amplifiers. differential amplifier 1.very high input impedence 2.very high bandwidth...
TRANSCRIPT
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DIFFERENTIAL AMPLIFIERS
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DIFFERENTIAL AMPLIFIER
1. VERY HIGH INPUT IMPEDENCE
2. VERY HIGH BANDWIDTH
3. DIFFERENTIAL INPUT
4. DC DIFFERENTIAL INPUT ACCEPTED
5. HIGH COMMON MODE REJECTION
6. SIGNAL INTEGRITY AT THE OUTPUT
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Let us start with a simple amplifier that can give us at the output a signal proportional to the difference between two signals, each with reference to a ground.
In a MOSFET under small signal conditions the output current is proportional to the signal voltage across the gate and source. As is obvious any signal applied to the source needs to be preferably applied through a buffer to reduce loading, while that at the gate could be applied directly.
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It is evident from the circuit diagram that when we consider the output at transistor M2, vo2, we are looking at a cascade of CD amplifier followed by CG amplifier from vs1 to vo2 and CS amplifier from vs2 to v02. Similarly considering the output at transistor M1, vo1, we are looking at a cascade of CD amplifier followed by CG amplifier from vs2 to vo1 and CS amplifier from vs1 to v01. Assuming a total symmetrical circuit, it is sufficient to analyze the effect of any one signal input to analyze the total circuit. In analyzing the circuit we will use superposition theorem.
Let us now look at the equivalent circuit and its analysis. We represent the current source ISS by its output impedance 1/go in the equivalent circuit.
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In the equivalent circuit
1s2gs1m1gs1mo1gs
L1gs1m1o
1s2gs1gs
vvgvgg1v
andRvgv
vvv
Solving for vo1/vs1 from the above three equations we get
o
1m
o
1m
L1m1s
2o
o
1m
o
1m
L1m1s
1o
g
g21
g
g
Rgv
vand
g
g21
g
g1
Rgv
v
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Let us define the following:
222s
2o12
2s
1o
211s
2o11
1s
1o
Av
v;A
v
v
andAv
v;A
v
v
We can then write
2s221s212o
2s121s111o
vAvAv
andvAvAv
For a symmetric network A11 = A22 and A12 = A21.
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We can now recast the equations as
2
RgAAAand
2
Rg
gg21
Rg
2AA
Awhere
2vv
AvvAv
2vv
AvvAv
Lo1211CM
L1m
om
L1m1211d
2s1sCM2s1sd2o
2s1sCM2s1sd1o
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The signal (vs1 – vs2) is called the differential signal and the signal (vs1 + vs2) is called the Common Mode signal. This leads us to define a very important parameter defining a differential Amplifier, the Common Mode Rejection Ratio, CMRR. CMRR is defined as
o
1mo1m
CM
dg
g
2
gg21
A
ACMRR
Having evaluated the gains of differential and common mode gain an interesting fall out is what is popularly known as half circuit equivalent.
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This has been reduced to two half circuits to evaluate differential and common mode gain. These are
Differential Common Mode
Half Circuit Half Circuit
2
RgAAAand
2
Rg
gg21
Rg
2AA
A
Lo1211CM
L1m
om
L1m1211d
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The load Resistance used in a CMOS circuit could be each a PMOS transistor in saturation with a constant Gate to Source Voltage or Gate tied to Drain.
In both these cases the load resistance is the same for M1 and M2.
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Let us now consider an non-symmetric load on M1 and M2 and look at the outputs vo1 and vo2. For this circuit we will have
om
om
3d
1m21
om
om
3d
1m22
om
om
3m
1m12
om
om
3m
1m11
gg21
gg
g
gA
gg21
gg1
g
gA
gg21
gg
g
gA
gg21
gg1
g
gA
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This will give us the outputs vo1 and vo2 as
21222CM12111CM
21222d
12111d
2s1s2CM2s1s2d2o
2s1s1CM2s1s1d1o
AAA;AAAand2
AAA;
2
AAAwhere
2
vvAvvAv
2
vvAvvAv
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Assuming that gm1 >> go, the values of Ad1, Ad2, ACM1 and ACM2 reduce to
3d
o2CM
3m
o1CM
3d
1m2d
3m
1m1d g2
gA;
g2
gA;
g2
gA;
g2
gA
Now since we are interested only in single ended output (say) vo2, we will device a useful method to use the other output to our advantage. What we would like to do is to connect the output vo1 to the gate of M4. We will then get the most commonly used single ended differential amplifier structure overleaf.
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Solving for the circuit assuming gm1 , gm3 >> go, gd1, gd3 we obtain the differential and common mode gain as
1do
3m1m
3d1d3m
1doCM
3d1d
1md
gg
gg2CMRRusGiving
ggg2
ggAand
gg
gA
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In our discussions so far we had considered NMOS input devices with PMOS load devices. It is equally likely that we may use PMOS input transistors and NMOS load transistors.
The relative advantages of the NMOS input differential Amplifier and PMOS input Differential Amplifier will be seen as we go down the course.
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NMOS input pair:
M5
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Common Mode Input Range
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Lowest common mode input voltage at gate of M1(M2)v G1(min) = V SS + v GS3 + v SD1 - v SG1
for saturation, the minimum value of v SD1 = v SG1 - |V T1 |Therefore, v G1(min) = V SS + v GS3 - |V T1 |
v G1(max) = V DD - v SD5 - v SG1
|V|VI
VminVor 1TO3TOSS
SS1G
|V|I
VVmaxVor 1TOSS
5SDDD1G
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Thermal Noise
21
11'P
33'N
21
111'P
2eq
LWK
LWK1
LWIK23
Tk16thv
To reduce thermal noise we choose
1
LWK
LWK
11'P
33'N
and large value of gm1.
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Assume that V DD = 3V and that V SS = -3V. Using K’N = 2K’P 18 A/V2, 0.8V <VTO3 , VT1< 1.2V, find the common mode range for worst case conditions. Assume that ISS = 100A, W1/L1 = W2/L2 = 5, W3/L3 = W4/L4 = 1, and vSD5 = 0.2V.
V25.08.02.118
1003
|V|VI
VminV 1TO3TOSS
SS1G
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V6.02.19x5
1002.03
|V|I
VVmaxV 1TOSS
5SDDD1G
The input common mode range is -0.25V to 0.6V.
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Slew Rate:
This defines the rate at which the load capacitor charged. In other words it defines the rate dv/dt at the output. Slew rate is a measure of the output to follow the input signal. This is normally associated with large signal property. Under large signal, only one of M1 or M2 will be ON and the charging current will be I5. This gives a slew rate CL(VDD- VSS)/I5.
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Parasitic elements in the Differential Amplifier:
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CT = tail capacitor (common mode only)
CM = mirror capacitor = Cdg1 + Cdb1 + Cgs3 + Cgs4 + Cdb3
COUT = output capacitor » Cbd4 + Cbd2 + Cgd2 + CL
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Noise Sources in Differential Amplifiers:
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Noise can be normally modeled as a current source in parallel to iD. This current source represents two sources of noise, thermal noise and flicker noise. The mean square current noise source is defined as
tCoefficienNoisekerFlicKF
ggffrequencyatBandwidthfwhere
fLCf
I)KF(
3
1gTk8i
mmbs
2ox
Dm2n
The mean square noise reflected to the gate giving mean square voltage noise at the gate
f
WLKCf
)KF(
g3
1Tk8
g
iv
'oxm
2m
2n2
eq
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The total output noise current, is obtained by summing each of the noise current contributions.
23eq2
1m
23m2
1eq2eq
24eq
23eq2
1m
23m2
2eq2
1eq2eq
2eq
21m
24eq
23m
23eq
23m
22eq
21m
21eq
21m
2to
v2g
gv2v
sTransistorPandNIdenticalgminAssu
vvg
gvvvwhere
vgvgvgvgvgi
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The total 1/f and thermal noise contributions can be written as
'P,Nox
P,N
21
11'P
33'N
21
111'P
2eq
2
3
1
P'P
N'N
11
p2eq
KC2
KFBwhere
LWK
LWK1
LWIK23
Tk16thv
LL
BK
BK1
LWf
B2f/1v
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2
3
1
P'P
N'N
11
p2eq L
L
BK
BK1
LWf
B2f/1v
To get the input noise for NMOS input stages interchange BP for BN, KN
’ for KP’ and vice versa.
Since BN = 5BP it is preferable to use PMOS input stage to reduce 1/f noise with large area for M1 and M2 and
1LL
BK
BK2
3
1
P'P
N'N
1/f Noise