Assignment Homework EE 435 Homework 6 Spring 2009 Problem 1 An open-loop amplifier has a gain Ao and left-half plane poles at p1 and p2 where p2=kp1 If it is used as a feedback amplifier with a feedback factor , determine the pole ratio k so that the feedback amplifier has a 65 degree phase margin. Problem 2 Assume an amplifier has a dc gain of 40,000, a pole at -30 rad/sec and a pole at -500,000 rad/sec. Assume this is used as a feedback amplifier with a of 0.5. a) Present a Nyquist Plot and from this determine the phase margin of this feedback amplifier. b) Determine the pole locations of the feedback amplifier c) Present a magnitude and phase plot of the open loop gain A(s) and from this determine the phase margin and compare with that obtained in part a). d) What is the gain-bandwidth product of the open-loop and the closed-loop amplifier? Compensate the amplifier by adjusting the low frequency pole so that the phase margin becomes 75 degrees. Problem 3 The amplifier given in the pervious problem and repeated below generally needs compensation. The compensated amplifier with internal compensation is shown below. For the compensated amplifier, determine the dc gain, approximate location of the dominant pole, the GB, and an expression for the value of CC needed to obtain a pole Q of .707 if = 1.
VDD
Q7 Q5 Q3 Vi+ Q1
Vb1 Vb2 Vb3
Q8 Q6 Q4 Q2 ViCC
Q10 VOUT CL
Vb4
Q9
Vb6
Q11
Problem 4 An analytical expression for the relationship between phase margin and pole Q for second-order lowpass amplifiers was given in class. Although analytical expressions are, in general, not possible for other structures, this relationship can be determined with computer simulations. a) Assume an amplifier with open-loop gain of
A (s ) =
10, 000 s s + 1 + 1 p 1 p2
Assume this is used to build a standard feedback amplifier that has gain of
A (s) =
A 1 + A
where is a constant. If =0.2 and p2=1000rad/sec, determine the location of the pole p1 so that the phase margin is 45o. What is the resultant pole Q of the feedback amplifier? Determine the location of the pole p1 so that the phase margin is 60o. What is the resultant pole Q of the feedback amplifier? b) Repeat part a) if the open-loop gain is given by
s 10, 000 + 1 z1 A (s) = s s + 1 + 1 p 1 p2
where z1= -500rad/sec c) Repeat part a) if the open-loop gain is given by
s 10, 000 + 1 z1 A (s ) = s s + 1 + 1 p 1 p2
c) where z1= + 500 rad/sec Repeat part a) if the open-loop gain is given by
A (s ) =
10, 000 s s p + 1 p + 1 1 2
3
d)
From the first 4 parts of this problem, what conclusions can be drawn about the relationship between the pole Q and the phase margin of feedback amplifiers?
Problem 5 Assume the operational amplifier below is being sold by a competitor and the competitor gives the circuit schematic but refuses to disclose any information about frequency response or anything about device sizes that are on the inside beyond stating that it has an open-loop dc gain of 80dB and that it is fabricated in a 0.5u CMOS process with parameters as described in the attachment. Assume you have measured the supply current when biased at a supply voltage of 5V and found it to be 10mA, that the load capacitance is 50pF, and that the output starts to distort when the output voltage exceeds 4.5V. Determine as many of the following as possible from the information given. If a parameter can not be determined from the information given, state that fact. a) W1/L1 b) W3/L3 c) GB d) SR e) VOMIN f) W9/L9 g) phase margin of the feedback amplifier if = 1.
VDD
M3
M4 VOUT
VIN
M1
M2
VIN 6
The CL
VB2
M9
Problem magnitude and phase plot of an operational amplifier are shown.
a) Determine the phase margin if this is used in a feedback amplifier with a feedback factor of =0.025 b) Is the feedback amplifier stable? Why? c) What is the maximum value of that can be used if the amplifier is to have a 60o phase margin? d) If = .001, what is the ideal closed loop gain and what is the percent closed-loop gain error due to the finite dc gain limitations of the op amp?
100 80
Gain Plot
Gain in dB
60 40 20 0 -20 -40 -60
1
10
10 2
10 3
10 4
10 5
0
1
10
102
103
104
105
Phase in degrees
-50 -100 -150 -200 -250 -300
Phase Plot
Problem 7 A two-stage operational amplifier is shown along with the device sizes in microns. Assume VDD=5V and VXX=1V a) Determine the dc gain of the op amp b) What is the GB of the op amp if CC=4pf and CL=1pf? Neglect all other capacitances in the amplifier c) Determine the power dissipation of the amplifier d) What is the pole Q if used in a noninverting feedback amplifier with =0.25? VDD
M3
M4 CC
M5 VOUT CL
V1
M1
M2
V2
VXX
M7
VXX
M6
Q1 Q2 Q3 Q4 Q5 Q6 Q7
W 300 300 400 400 700 250 350
L 1 1 1 1 1 1 1
Problem 8 If a feedback amplifier has a characteristic polynomial given by 3 DFB (s) = s + 2s 2 + as + 60 where a is a variable, what is the minimum value of a that can be used if the feedback amplifier is to remain stable? Problem 9 Assume an operational amplifier has a dc gain of 80dB, three poles in the LHP of magnitudes 10rad/sec, 4Krad/sec and 30krad/sec. If the position of a zero can be adjusted in a way that the dc gain and all poles remain fixed, plot the phase margin versus the location of the zero as it is moved from 10K rad/sec in the RHP to -10K rad/sec in the LHP.
Problem 10 A network that can be used as the network for a feedback amplifier is shown. The blue arrow shows the intended direction of propagation of the feedback signal through the feedback network. 2
2 1
1
a) b) c)
Determine the of this network if the overall feedback amplifier is a voltage amplifier Determine the of this network if the overall feedback a...