9. W27
L27
The output current available can be found by assuming that vin = vi1-vi2 0.
i1 + i2 = I5 + A(i2-i1)
The ratio of i2 to i1 can be expressed as
i2
i1 = exp
10.
11. vin
nVt
If the output current is iOUT = b(i2-i1) then combining the above two equations gives,
iOUT =
bI5
exp
20. gm12e
2
n1+gm22e
2
n2+gm32e
2
n3+gm42e
2
n4+(e
2
n8/rds12)+(e
2
n9/rds22)
Divide by (gm1RIgm6RII)2 to get the eq. input-noise voltage spectral density, e
2
eq, as
e
2
eq =
e
2
to
(gm1gm6RIRII)2 =
2e
2
n6
2
n1
gm12RI2 + 2e
1+
gm3
gm1
29. Lecture 290 – Low Power and Low Noise Op Amps (3/28/10) Page 290-19
1/f Noise of a Two-Stage, Miller Op Amp
Consider the 1/f noise:
Therefore the noise generators are replaced by,
e
2
ni =
B
fWiLi
(V2/Hz) and i
2
ni =
2BK’Ii
fLi2 (A2/Hz)
Therefore, the approximate equivalent input-noise voltage spectral density is,
e
2
eq = 2e
2
n1
2 (V2/Hz)
37. 2 =
1+
120·1.33
25·1.67
2
1
20
3.33x10-12
f 1.0365 =
3.452x10-12
f (V2/Hz)
Note at 100Hz, the voltage noise in a 1Hz band is 3.45x10-14V2(rms) or 0.186μV(rms).
3.) The thermal noise at room temperature is
e
2
n1 =
8kT
3gm =
8·1.38x10-23·300
3·500x10-6 = 2.208x10-17 (V2/Hz)
which gives
e
2
eq = 2·2.208x10-17