1 a

ECE137B Final Exam

6/11/2015, 8-11AM.

There are 4 problems on this exam and you have 3 hours

There are pages 1-21 in the exam: please make sure all are there.

Do not open this exam until told to do so.

Show all work.

Credit will not be given for correct answers if supporting work is not shown.

Class Crib sheets and 3 pages (front and back→ 6 surfaces) of your own notes permitted.

Don’t panic.

Time function LaPlace Transform

)(t 1

U(t) 1/s

)(tUe t

s

1 or

/1

/1

s

)(cos tUte d

t

22

ds

s

)(sin tUte d

t

22

d

d

s

Name: _________________________________

Problem points possible Problem points possible

1a 5 2c 5

1b 5 3a 10

1c 15 3b 10

1d 10 4a 10

1e 5 4b 10

2a 5

2b 10 total

2 a

Problem 1, 40 points

frequency reponse, negative feedback

In the circuit above 21 mm gg =20mS. 3mg 100mS, 1R =1k , 2R 9 k .

3R 10 k , infinity DSR for all FETs

21 gsgs CC 127 fF, 21 gdgd CC 0fF, 3gsC 0 fF, 3gdC =159fF.

Note: simplify the problem by using the approximation shown above right.

Part a, 5 points

feedback relationships

In the relationship T

TAACL

1, what is A for this circuit ?

A =__________________

3 a

Part b, 5 points

feedback relationships

Find the value of the loop transmission at DC and the closed loop gain at DC.

Hint---I recommend using the indicated cut point.

T =__________________ CLA =__________________

4 a

Part c, 15 points

transistor circuit frequency reponse.

Find the first two pole frequencies of the loop transmission T .

1pf =__________________ 2pf =__________________

5 a

6 a

Part d, 10 points

loop bandwidth and stablity.

Plot the loop transmission (labels slopes, label critical frequencies)

Determine the loop bandwidth and phase margin

loopf _____________________, phase margin =_____________________

Draw the loop transmission T on this plot

100 104

106

108

1010

-40

-20

0

20

40

60

80

100

120

Frequency, Hz

7 a

8 a

Part e, 5 points

closed-loop bandwidth

Plot the closed-loop gain vs. frequency, estimating the gain peaking at loopf

Estimate the amplifier's closed loop bandwidth

closed-loop bandwidth =_____________________

Draw the closed loop gain on this plot

100 104

106

108

1010

-40

-30

-20

-10

0

10

20

30

40

Frequency, Hz

9 a

Problem 2, 20 points

Circiut frequency response by MOTC.

In the circuit above 1mg =10mS, 2mg =50mS.

genR =1000 , 1gsC =15.9fF, 2gsC =79.5fF 21 gdgd CC 0fF.

infinity DSR for both FETs

LR 1 k .

part a, 5 points

midband analysis

find the gain Vout/Vgen at low frequencies. Vout/Vgen=_____________________

10 a

part b, 10 points

frequency reponse analysis

Find 1a , 2a . If the poles are real, find 1pf and 2pf ; if they are complex, find nf and

1a =____________________ 2a =_________________

real poles: 1pf =__________________ 2pf =____________________

complex poles nf =___________________ =______________

11 a

12 a

part c, 5 points

another frequency reponse analysis

Using any correct method, find the transfer function Vout(s)/Vgen(s).

The answer must be in standard form 2

21

1

1

.1

)(

)(

sasa

sb

V

V

sV

sV

DCgen

out

gen

out

Hint: Nodal analysis will be slow and painful.

1R =1k , 2R =1k , 1C =1nF, 2C =2nF, 3C =3nF

DCgen

out

V

V__________________ , 1a _________________ , 2a _________________

1b _________________

13 a

14 a

Problem 3: 20 points

negative feedback and stability

In the circuit above, 2dA and 3dA are ideal, infinite-gain op-amps.

1dA is a differential amplifier with a voltage gain of 1.

1R =1 k , 2R =4k , 1C =15.9pF, 2C =15.9pF.

Part a, 10 points

simple nodal analysis

find the loop transmission )(sT .

The answer must be in standard form: ...1

...1)(

2

21

2

21

sasa

sbsbTsT DC ,

or if there are N poles at DC, ...1

...1

)(

1)(

2

21

2

21

sasa

sbsb

ssT

N

)(sT _____________________________________________________

15 a

16 a

Part a, 10 points

feeback stability analysis

Plot the loop transmission (labels slopes, label critical frequencies)

Determine the loop bandwidth and phase margin

loopf _____________________, phase margin =_____________________

Draw the loop transmission T on this plot

100 1000 104

105

106

107

108

109

-40

0

40

80

120

Frequency, Hz

T,

dB

17 a

Problem 4, 20 points

frequency and transient response

part a, 10 points

transient response

A circuit has the response to a 1V step-function input:

-0.5

0

0.5

1

1.5

2

-5 10-9

0 5 10-9

1 10-8

1.5 10-8

2 10-8

2.5 10-8

3 10-8

Vo

ut(

t)

time, seconds

Determine the frequency and damping factor of the dominant poles of the transfer function.

Natural resonant frequency = ______________ Hz

estimated damping factor = __________________

18 a

19 a

part b, 10 points

transient response

-0.2

0

0.2

0.4

0.6

0.8

1

0 2 10-7

4 10-7

6 10-7

8 10-7

1 10-6

Vo

ut(

t)

time, seconds

(1)

-0.5

0

0.5

1

1.5

2

-5 10-9

0 5 10-9

1 10-8

1.5 10-8

2 10-8

2.5 10-8

3 10-8

Vo

ut(

t)

time, seconds

(2)

-0.2

0

0.2

0.4

0.6

0.8

1

0 2 10-7

4 10-7

6 10-7

8 10-7

1 10-6

Vo

ut(

t)

time, seconds

(3)

-0.2

0

0.2

0.4

0.6

0.8

1

0 2 10-7

4 10-7

6 10-7

8 10-7

1 10-6

Vo

ut(

t)

time, seconds

(4)

You have four unknown circuits (1-4) whose response to a 1V step-function is as above.

For each, you must identify, giving your reasons clearly, which possible circuits (a-e) might give

this observed resonse. (Consider the possibility that some elements in the circuits a-e might

have negligible values)

20 a

response #1: circuits ________________________________

why:

response #2: circuits ________________________________

why:

response #3: circuits ________________________________

why:

response #4: circuits ________________________________

why:

21 a