Question 3 – Transfer Functions

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```					ENGR4300                   Test 3S                   Fall 2005

ENGR4300
Fall 2005
Test 3S

Name _______solution___________

Section________________________

Question 1 (25 points)___________

Question 2 (25 points) ___________

Question 3 (25 points)___________

Question 4 (25 points)___________

Total (100 points): ______________

Please do not write on the crib sheets.
On all questions: SHOW ALL WORK. BEGIN WITH FORMULAS, THEN
SUBSTITUTE VALUES AND UNITS. No credit will be given for
numbers that appear without justification.

1 of 12
ENGR4300                                  Test 3S                               Fall 2005

Question 1 – Astable Multivibrator (25 points)

The multivibrator above was built with the 555 timer chip shown. In the diagram, Vs is
the source voltage, Vc is the voltage across the capacitor C1, and VD is the voltage at the
discharge pin of the timer. You are given the following component values:
Test A: R1 = 4.7k ohms R2 = 6.8k ohms C1 = 0.68F Vs = 6V
Test B: R1 = 2.2k ohms R2 = 4.7k ohms C1 = 1.5F                Vs = 12V
Test C: R1 = 6.8k ohms R2 = 8.6k ohms C1 = 0.47F Vs = 5V

1) Calculate the on time and off time of the multivibrator. (4 pt)

T1  0.693( R1  R2)C1           T1 = 0.693(4.7K+6.8K)(0.68) = 5.42ms
T 2  0.693( R2)C1             T2 = 0.693(6.8k)(0.68) = 3.20ms

Test A: Ton = 5.42ms Toff = 3.20ms
Test B: Ton = 7.17ms Toff = 4.89ms
Test C: Ton = 5.02ms Toff = 2.80ms

2) Calculate the frequency and period of the multivibrator. (4 pt)

T=Ton + Toff     f=1/T          T=5.42m+3.20m = 8.62ms f=1/8.62m=116Hz

Test A: T = 8.62ms f = 116 Hz
Test B: T = 12.06ms f = 82.9 Hz
Test C: T = 7.82ms f = 128 Hz

3) Calculate the duty cycle of the multivibrator. (2 pt)

DC = 100*Ton/T           DC=100*5.42m/8.62m=62.9%

Test A: DC = 62.9%
Test B: DC = 59.5%
Test C: DC = 64.2%

2 of 12
ENGR4300                                 Test 3S                                 Fall 2005

4) In theory, what are the maximum and minimum voltage across the capacitor, Vc? (2
pt)
Vmin = Vs/3 Vmax = 2*Vs/3 Vmin=6/3=2V Vmax = 2*6/3 = 4V

Test A: Vmin = 2V Vmax = 4V
Test B: Vmin = 4V Vmax = 8V
Test C: Vmin = 1.67V Vmax = 3.33V

5) When the transistor inside the 555 timer is closed, the output at pin 7 is grounded, and
therefore, equal to zero. When the transistor is open, the output at pin 7 can be found
using the voltage divider formed by R1 and R2. Find an expression for the voltage at pin
7 (when pin 7 is not grounded) in terms of the voltage across the capacitor, Vc, the source
voltage, Vs, and the two resistors R1 and R2. [Hint: Recall how you calculate the voltage
at the non-inverting input for a Schmitt trigger.] Do not substitute values. (3 pt)

 R2 
VD            VS  VC   VC
 R1  R 2 
This can be simplified further, but it is not necessary.

6) Use the equation in 5) to find the maximum and minimum voltage at pin 7 when the
transistor is open. (2 pt)

VDlow = [6.8k/(6.8k+4.7k)](6-2) + 2 = 4.36V
VDhigh = [6.8k/(6.8k+4.7k)](6-4) + 4 = 5.18V

Test A: VDlow = 4.36V      VDhigh = 5.18V
Test B: VDlow = 9.44V      VDhigh = 10.72V
Test C: VDlow = 3.53V      VDhigh = 4.27V

7) On the graph below, identify the outputs at pin (2, 6), 7 and 3 of the multivibrator.
Identify both parts of the cycle for each. (6 pt)

This shows the basic shape of the signals. The image on each test was different.
3 of 12
ENGR4300                                           Test 3S                                       Fall 2005

Question 2 – Combinational Logic Circuits (25 points)
Test A and B:
1) You are given the following circuit
U11A
1
3   C                             2
U3A

A                       2
3
1
F
7432
7402

U13A
1

2
3
E
7486

U5A
U1A                                      1
1
3                                 2
3
G
B                           2
D                                  7408
7400

a) Fill out the truth table below (10 pt)

A             B           C              D         E           F       G
0             0           0              1         1           0       1
0             1           1              1         0           0       0
1             0           1              1         0           0       0
1             1           1              0         1           0       0

b) What gate is the output at G equivalent to (circle one)? (1 pt)

AND        NAND              OR       NOR       XOR         XNOR        NOT

2) Fill out the truth table below to prove the following relationship: (14 pt)

                   
if Q  A  B  A  B   A  B  then Q  A  B

A         B         A                  B       A B          A B    A B           Q          A+B
0         0         1                 1        0         0           0              0          0
0         1         1                 0        1         0           0              1          1
1         0         0                 1        0         1           0              1          1
1         1         0                 0        0         0           1              1          1

4 of 12
ENGR4300                                               Test 3S                                        Fall 2005

Test C:
1) You are given the following circuit
U5A
1
3   C                               2
U3A

A                               2
3
1
F
7408
7402

U1A
1

2
3
E
7400

U5A
U13A                                       1
1
3                                   2
3
G
B                           2
D                                       7408
7486

a) Fill out the truth table below (10 pt)

A             B               C          D             E           F         G
0             0               0          0             1           0         0
0             1               0          1             1           0         1
1             0               0          1             1           0         1
1             1               1          0             1           0         0

b) What gate is the output at G equivalent to (circle one)? (1 pt)

AND        NAND                 OR        NOR       XOR            XNOR       NOT

2) Fill out the truth table below to prove the following relationship: (14 pt)

                       
if Q  A  B  A  B   A  B  then Q  A  B

A         B         A                B         A B          A B            A B      Q              A B
0         0         1               1          1             1               0         0              0
0         1         1               0          1             0               1         0              0
1         0         0               1          0             1               1         0              0
1         1         0               0          1             1               1         1              1

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ENGR4300                                        Test 3S                                                     Fall 2005

Question 3 – Sequential Logic Gates (25 points)

Quiz A and B:
You are given the following circuit DSTM1 provides the clock for the counter. DSTM 1
provides the clock to the two flip flops. DSTM2 provides an initial reset pulse to all the
sequential chips. Therefore, you can assume that QA, QB, QC, QD, Q1, and Q2 are all
initially low.
U1A
DSTM1
CLK                                             1         2

7404

U3A                                                         U6A
1                    3                                        1
A       QA                                                 J
QB
4
5                                        12              Q
3         Q1
CLR

QC   6                          U4A                CLK            2
QD                      1             2       4               Q

CLR
74393                                            K
7404                        74107
2

13
U7A
1
J
12              Q
3         Q2
U5A               CLK            2
1             2   4               Q

CLR
K
U2A                                           7404                    74107
DSTM2

13
CLK                     1                2

7404

1) Sketch the timing trace for each of the signals shown. (14 pt)

6 of 12
ENGR4300                                        Test 3S                                                     Fall 2005

Quiz C:
You are given the following circuit DSTM1 provides the clock for the counter. DSTM 1
provides the clock to the two flip flops. DSTM2 provides an initial reset pulse to all the
sequential chips. Therefore, you can assume that QA, QB, QC, QD, Q1, and Q2 are all
initially low.
U1A
DSTM1
CLK                                             1         2

7404

U3A                                                         U6A
1                    3                                        1
A       QA                                                 J
QB
4
5                                        12              Q
3         Q1
CLR
QC   6                          U4A                CLK            2
QD                      1             2       4               Q

CLR
74393                                            K
7404                        74107
2

13
U7A
1
J
12              Q
3         Q2
U5A               CLK            2
1             2   4               Q

CLR
K
U2A                                           7404                    74107
DSTM2

13
CLK                     1                2

7404

1) Sketch the timing trace for each of the signals shown. (14 pt)

7 of 12
ENGR4300                                  Test 3S                                 Fall 2005

2) We take the output of this circuit and use it as the input to the transistor circuit shown
below:

Quiz A                                     Quiz B and C

Fill in the following table for all possible values of Q1 and Q2. (4 pt)
Quiz A                                           Quiz B and C

Q1    Q2    Vout                                Q1    Q2    Vout
0V    0V    5V                                  0V    0V    5V
0V    5V    5V                                  0V    5V    0V
5V    0V    5V                                  5V    0V    0V
5V    5V    0V                                  5V    5V    0V

3) What are the values of the signals at Q1, Q2 and Vout after 8.9 milliseconds? (3 pt)

All Tests:           Q1: 0V           Q2: 0V         Vout: 5V

8 of 12
ENGR4300                                 Test 3S                               Fall 2005

Quiz A and B
4) IC chips have a standard numbering convention that you should now know. Label pins
#1-8 on the IC below. (HINT: It doesn’t matter what the chip’s function is – just label
#1, #2, …). (1 pt)

5) Like op-amps, IC chips need two power connections in order to function. Label the
power (Vcc) and ground pins on the 7404 IC chip pictured below with the appropriate
voltage values. (1 pt)

6) The 7404 chip contains more than one inverter. How many does it contain? (1 pt)

6

7) You’ve primarily used two types of capacitors in the studio: electrolytic and ceramic
disc, each shown below:

Electrolytic:                                         Ceramic Disc:

Which one is polarized (e.g. has a + and – lead) (circle one)? (1 pt)

neither          electrolytic           ceramic disc           both

9 of 12
ENGR4300                                 Test 3S                                Fall 2005

Quiz C
4) IC chips have a standard numbering convention that you should now know. Label pins
#1-8 on the IC below. (HINT: It doesn’t matter what the chip’s function is – just label
#1, #2, …). (1 pt)

5) We’ve talked about the use of bypass capacitors when working with digital logic
chips. Which answer below best describes where they should be located and why we use
them? (1 pt)

a. Place one or more between digital logic inputs and ground to smooth the sharp
transients of digital switching signals that could otherwise corrupt proper chip
operation.
b. Place one or more in series with logic power (Vcc) where it enters the protoboard to
filter noise coming from the power supply.
c. Place one or more in parallel with Vcc and ground at each chip to filter noise.
d. Place only one between Vcc and high speed logic chip outputs to suppress output
oscillation (e.g. ringing).

6) What was the recommended range of bypass capacitor values given for the TTL logic
family used in the studio? (circle one) (1 pt)

a) 0.1pF – 0.5pF       b) 0.01nF – 0.1nF        c) 0.01uF – 0.1uF         d) 0.1uF – 10uF

e) 10uF – 100uF            f) I don’t know because I slept through that lecture.

7) You’ve primarily used two types of capacitors in the studio: electrolytic and ceramic
disc, each shown below:

Electrolytic:                                         Ceramic Disc:

Which one is polarized (e.g. has a + and – lead) (circle one)? (1 pt)

neither          electrolytic           ceramic disc           both

10 of 12
ENGR4300                                  Test 3S                              Fall 2005

Question 4 – Switching Circuits (25 points)

_

+

_
+
+

Quiz A: V1=4V V3= -10V V4=2V V5=8V R4=30k R5=2k
Quiz B: V1=6V V3= -8V V4=3V V5=10V R4=20k R5=1k
Quiz C: V1=5V V3= -7V V4=2V V5=9V R4=40k R5=2k

1) In the circuit shown, circle the model of a Schmitt trigger. (1 pt)

2) What is the reference voltage of the Schmitt trigger model? (1 pt)

Test A: Vref = 2V       Test B: Vref = 3V      Test C: Vref=2V

3) If the op-amp is putting out its maximum voltage at C, what is the voltage at point B,
the non-inverting input to the op-amp? (3 pt)

 R2 
 R  R (vout  Vref )  Vref
v                                          v+ = [2k/(2k+30k)](8-2) +2 = 2.375V
 1    2 

Test A: v+ = 2.38V      Test B: v+ = 3.33V     Test C: v+ = 2.33V

4) If the op-amp is putting out is minimum voltage at point C, what is the voltage at point
B, the non-inverting input to the op-amp? (3 pt)

 R2 
 R  R (vout  Vref )  Vref
v                                          v+ = [2k/(2k+30k)](-10 -2) +2 = 1.25V
 1    2 

Test A: v+ = 1.25V      Test B: v+ = 2.48V     Test C: v+ = 1.57V

11 of 12
ENGR4300                                 Test 3S                                Fall 2005

5) On the following plot, the input at point A is shown.

a) Mark the upper and lower thresholds of the hysteresis (2 pt), and
b) sketch and label the output at points B, C, D and E for the input shown. (12 pt)

Many of the signals will overlap. Use the PSpice labeling convention to identify the
signals by drawing unique symbols on important parts of each trace. Note that the input
has a little box. Use the following: B = + C =  D =  and E = .

This plot shows the basic shape of the signals for all three tests. Specific high and low
values are given below.

Test A: Signals change when input rises above 2.38V or falls below 1.25V
Signal B toggles between 1.25 and 2.38 volts. (H-L-H-L-H)
Signal C toggles between +8V and -10V (H-L-H-L-H)

Test B: Signals change when input rises above 3.33V or falls below 2.48V
Signal B toggles between 2.48 and 3.33 volts. (H-L-H-L-H)
Signal C toggles between +10V and -8V (H-L-H-L-H)

Test C: Signals change when input rises above 2.33V or falls below 1.57V
Signal B toggles between 1.57 and 2.33 volts. (H-L-H-L-H)
Signal C toggles between +9V and -7V (H-L-H-L-H)

All Tests: Signal D toggles between 0V and some voltage less than 5V (L-H-L-H-L)
(You do not know enough about diodes to know the exact voltage, so we
accepted anything in this range that was recognizable as not zero.)
Signal E is constant at 5V

8) Are the LEDs on or off at the following times (3 points)?
time           LED1             LED2
0.3ms          ON               ON
0.8ms          OFF              ON
1.2ms          ON               ON

12 of 12

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