ECE595A Exam 2 (April 20 2006)



ECE595B Exam 2 (Nov 19 2007)

Purdue ID:

Full Name:

This is an open book open notebook test. You are allowed to use a calculator. All work and answers should be written in the space provided.

State any assumption you make. It is recommended to keep your answer clear and concise.

At the end of test period (55min), turn in all test pages. You will be given a five minute warning prior to the end of the test period. Once the proctor leaves the exam room, no more test pages will be accepted.

|Problem |Score |

|1 | / 25 |

|2 | / 25 |

|3 | / 25 |

|4 | / 25 |

|Total | / 100 |

1. [25 points] Consider the common source amplifier shown below. The input is connected to the body. Assume M1 is in saturation and ro >> RD.

a) [12 points] Derive the expression for the low frequency gain [(out/(in].

b) [13 points] Now the source is degenerated using Rs. Derive the expression for the low frequency gain [(out/(in] again.

2. [25 points] Consider the fully differential amplifier shown below. Assume the input signal is symmetric, there is no transistor mismatch, and all transistors are in saturation.

a) [13 points] Ignoring the signal source impedance, the differential input to the differential output transfer function, H(s), has two poles. Derive the expression for the low-frequency gain (AM), the first pole((P1), and the second pole((P2). Include Cgs, Cdb, Csb, but ignore Cgd. Use Cgsx, Cdbx, and Csbx where x is the number of each transistor.

b) [12 points] During fabrication, a parasitic series R-C is accidentally inserted as shown in the figure. Derive the expression for the low-frequency gain (AM), the first pole((P1), and the second pole((P2), again. Assume R is very small, and can be ignored for gain and pole analysis. Assume also that the C is very small and comparable with Cdb.

[Hint: Only one of the three parameters (AM / (P1 / (P2) is affected.]

3. [25 points] Consider the common source amplifier shown below. Cc is a coupling capacitor. Because of the bandpass characteristic, we can ignore flicker noise. Ignore the noise from the bias network.

a) [13 points] Calculate the output noise voltage, [pic], in mid-band. [HINT: You don’t need to calculate the input-referred noise voltage or current. Simply calculate the output noise voltage for the given circuit configuration. Include the noise from Rs.]

b) [12 points] Assume a genius Purdue grad student who took ECE595B invented resistors that can have correlated noise sources. Using the new resistors, the amplifier has been designed again. Using the polarity of each noise source shown below, the correlation coefficient between [pic] and [pic] is designed to be “+1” – fully correlated. Note that the drain current noise is not correlated. Calculate the output noise voltage, [pic], in mid-band, again.

4. [25 points] Consider the switched capacitor circuit shown below. The two switches and one capacitor in the dotted line can be modeled as a resistor (Req) in discrete time domain. [13 points] Calculate the equivalent resistance, Req. [12 points] Calculate the slope of the transfer function magnitude vs. ( curve. Note that the plot uses log-log scale. Assume the op-amp is ideal.

-----------------------

Freq

|H(s)|

AM

VBias

Network

(in

RD

(out

M1

CC

RS

M4

(o+

C

R

Vdd

M2

(in

RS

RD

[pic]

(out

(out

C2

S2

S1

M3

vBias2

vBias1

(o-

M1

M6

M5

AM

|H(s)|

Freq

(in+

(P1

(P2

(in-

M1

[pic]

VBias

Network

CC

Slope?

|H|

(

CK

CK

C1

fCK = 1 MHz

C1 = 2 pF

C2 = 10 pF

Req

(In

(out

RD

(out

M1

M1

vBias

vBias

(in

RD

(in

gm : Transconductance

gmb : Body transconductance

RS

(P2

Midband

(o-

(o+

Fully correlated

(P1

(P3

Vdd

M2

M1

M6

M5

(in-

(in+

vBias1

vBias2

M4

M3

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