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# CMOS Analog IC Design: Problems and Solutions

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Nguyễn Gia Hào

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## MASTER IN MANAGEMENT

### Basic Gain Stages

E-2: The output resistance of the common-drain stage, where the gain transistor has source and ground connected, is of the order of 1/gm. F-11: The output resistance of a common-source stage biased by an active load is of the order of rds. J-6: The output resistance for a telescoping cascode preset by an ideal current source is of the order of gmr2ds.

## RUN FASTER

Use LTspice to find the output voltage range for RL=5 kΩ, assuming that the voltage across the current source IB must be at least 0.3 V. To find the small-signal gain and output resistance, we draw the small-signal diagram shown below corresponding to Problem 4.6. The small-signal open-circuit voltage gainAvoc is found as vo/vinwithRL=∞, i.e. RLeave from the small-signal diagram.

From the graph, we find the minimum value of the output voltage to be vOmin=−0.192 V, and from the requirement that the voltage at the current source IB must be at least 0.3 V, we find the maximum output voltage to be vOmax= 0.6 V. For the telescoping cascode shown above, use LTspice to find the input bias value VIN required to give an output bias voltage of 0.9 V. Find the small-signal resistance to ground from the node X between the source of M2 and the drain of M1 and find the small-signal voltage gain from the input to node X.

## SETASIGNThis e-book

### Multistage Amplifiers

The small-signal low-frequency differential gain of the op amp shown above is approximately A: 61 dB. Assuming all transistor capacitances are much less than 1 pF, the frequency of the dominant pole in the opamp above is approx. Assuming all zeros and non-dominant poles have frequencies above 1 GHz, the unity gain frequency of the op amp shown above is approx.

For the folded cascode opamp shown above, assume that all transistors have a channel length L=1 µm and a channel width W =20 µm. Calculate the low-frequency small-signal differential gain and the -3 dB bandwidth for a load capacitance of CL=1.5 pF, which is much larger than the parasitic transistor capacitances. The low-frequency small-signal gain Adis found fromAd=gm1rout=gm1/goutwhereroutis found from Eq.

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