Chapter 9-Operational Amplifier

Operational Amplifier
Telescopic cascode op amps design example (1)
Specifications: VDD=3V Differential output swing = 3 V Power dissipation = 10 mW Voltage gain = 2000 Other parameters (effective channel length=0.5 m): nCox =60A/V2 pCox =30A/V2 n=0.1V-1 p=0.2V-1 Voltage gain=2000 =0 VTHN=|VTHP|=0.7V
Operational Amplifier
Performance Parameters-gain (2)
Solution:
Av, no minal 1/ ( R1 R2 ) / R2 10
Av , closed A1 1 1 (1 ) {onlyif A1 1} 1 A1 A1
Performance Parameters-small-signal bandwidth (4)
For a step input Vin=au(t):
Vout (t ) a 1

t [1 exp( )]u (t )

When t, the final output value:
VF a 1
Since M1~M4 are in signal path, keep sizes unchanged first, therefore double the length of M5~M8 while keep their W/L unchanged: (W/L)1-4=1250 (Leff=0.5 m) (W/L)5-8=1111 (Leff=1.0m) (W/L)9=400 The gain can be re-calculated as,
In a one-pole system (dominant pole of 0):
Av A0 A 0 0 1 s / 0 j {when 0 }
Av 1
u A00
or
fu A0 f 0
So, in a one-pole system, fu=GBW (gain-bandwidth) Although in multi-poles systems, fuGBW, GBW is still used to design the circuit.
Av , closed Av ,no min al Av ,no min al
Gain error:

1 1% A1
A1
1 10010 1000 1%
Means that once the open-loop gain (A1) larger than 1000, the closed-loop gain always keeps constant value of 10, and with the error within 1%
Fig.9.6 (a): Single-ended differential pair with active current mirror as load, this topology adds one mirror pole; Fig 9.6 (b): Fully differential pair; For deep sub-micron technology, the gain usually hard to exceed 20.
Operational Amplifier
Performance Parameters-small-signal bandwidth (3)
Refer to Fig. 8.9 in P.253:
A0 Vout 1 A0 (s) s Vin 1 (1 A0 )0
Where:

Operational Amplifier
Performance Parameters-others Output swing;
Linearity;
Noise and offset; Supply Rejection.
Operational Amplifier
One-stage Op Amps (1)
Operational Amplifier-One-stage Op Amps (3)
Overdrive voltage M4 in saturation Vout > Vb-VTH4 M2 in saturation Vout < Vb-VGS4+VTH2; Output swing (Vb -VGS4+VTH2)-(Vb -VTH4)= VTH4- (VGS4-VTH2), very small, so not suitable for unity-gain connection!.
Operational Amplifier
Telescopic cascode op amps design example (2)
First consider power P=10 mW, therefore the total current: I=P/VDD=3.33mA Allocating 3mA to M9 and 330A to Mb1 and Mb2 Second consider output swing: Swing VXY=3V SwingVX=SwingVY=1.5V VDD=3V |VOD7|+|VOD5|+VOD3+VOD1+VOD9=1.5V ID9 largest, allocate VOD9=0.5V P< n, VODP should be larger than VODN |VOD7|=|VOD5|=0.3V and VOD3=VOD1=0.2V
Operational Amplifier
Performance Parameters-gain (1)
A1
Question: If the nominal （标称）gain (R1+R2)/R2=10 Determine the minimum value of A1 for a gain error of 1%?
GBW A0 f 0 A00 1 1 9.21Grad / s 1.47GHz 2 2 2
Operational Amplifier
Performance Parameters-Large-signal bandwidth
CL
If CL is large, when Vin change from 0 to 1V, Vout cannot change instantaneously and still keep 0V, the signal feedback to negative input of A(s) is also 0V; Therefore the differential input signal of A(s) will reach to 1V, if the gain of A(s) larger than 1000, then the output of A(s) will be larger than 1000V; Large-signal, system non-linear, need to simulate carefully.
Operational Amplifier
Telescopic cascode op amps design example (3)
Use initial bias guess, the W/L of all transistors can be calculated as:
(W/L)1-4=1250 (W/L)5-8=1111 (W/L)9=400 Assuming all transistors minimum length of 0.5 m ,
Operational Amplifier
Performance Parameters-gain (3)
If not use feedback system, Fig.9.3 can also obtain a gain of 10 by using a simple common-source stage. However, the typical gain error will be larger than 10% very easily because of the fabrication error.
Operational Amplifier
Performance Parameters-small-signal bandwidth (2)
A( s uestion: Assume the op amp is a single-pole voltage amplifier. If Vin is a small step, calculate the time required for the output voltages to reach within 1% of its final value. What unity-gain bandwidth must the op amp provide if 1+R1/R210 and the settling time is to be less than 5ns? For simplicity, assume the low-frequency gain is much greater than unity.

For 1% settling, Vout=0.99VF, and hence