Download 10-1. Determine the Nyquist sample rate for a maximum analog

10-1. Determine the Nyquist sample rate for a maximum analog input frequency of
a. 4 kHz.
b. 10 kHz.
a. 8 kHz
b. 20 kHz
10-2. For the sample-and-hold circuit shown in Figure 10-5a, determine the largest-value
capacitor that can be used. Use the following parameters: an output impedance for Z1 = 20 , an
on resistance of Q1 of 20 , an acquisition time of 10 s. a maximum output current from Z1 of
20 mA, and an accuracy of 1%.
C = 0.0543 μF
10-3. For a sample rate of 20 kHz, determine the maximum analog input frequency.
10 kHz or less
10-4. Determine the alias frequency for a 14-kHz sample rate and an analog input frequency of
8 kHz.
6 kHz
10-6. Determine the minimum number of bits required in a PCM code for a dynamic range of
80 dB. What is the coding efficiency?
14 bits, coding efficiency = 94.91%
10-8. Determine the SQR for a 2-vrms signal and a quantization interval of 0.2 V.
SQR = 1200 or 30.8 dB
10-10. A 12-bit linear PCM code is digitally compressed into eight bits. The resolution = 0.03
V. Determine the following for an analog input voltage of 1.465 V:
a. 12-bit linear PCM code
+49 or 100000110001
b. eight-bit compressed code
10101000
c. Decoded 12-bit code
100000110001
d. Decoded voltage
+1.47 V
e. Percentage error
Qe only = 0.005, 0.341%
10-12. For each of the following 12-bit linear PCM codes, determine the eight-bit compressed
code to which they would be converted:
a. 100000001000
10001000
b. 100000001001
10001001
c. 100000010000
10010000
d. 000000100000
0010000
e. 010000000000
01110000
f. 010000100000
01110000
10-14. For the sample-and-hold circuit shown in Figure 10-5a, determine the largest-value
capacitor that can be used for the following parameters: Z1 output impedance = 15 , an on
resistance of Q1 of 15 , an acquisition time of 12 s, a maximum output current from Z1 of 10
mA, an accuracy of 0.1%, and a maximum change in voltage dv = 10 V.
0.012 μF
10-16. Determine the alias frequency for the following sample rates and analog input
frequencies:
fa(kHz)
fs(kHz)
ffo(kHz)
3
4
1
5
8
3
6
8
2
5
7
2
10-18. Determine the minimum number of bits required for PCM codes with the following
dynamic ranges and determine the coding efficiencies: DR = 24 dB, 48 dB, and 72 dB.
DR
bits
efficiencies
24 dB
5
81.5%
48 dB
8
99.7%
72 db
12
99.7%
10-20. For the following resolutions, determine the range of the eight-bit sign-magnitude PCM
codes:
Code
Resolution (V)
Range
10111000
0.10
+5.55 to +5.65
00111000
0.10
-5.55 to –5.65
11111111
0.05
+6.325 to +6.375
00011100
0.02
-0.55 to –0.57
00110101
0.02
-1.05 to –1.07
11100000
0.02
+1.91 to +1.93
00000111
0.02
-0.13 to -0.15
10-22. Determine the resolution and quantization noise for an eight-bit linear sign-magnitude
PCM code for the following maximum decoded voltages: Vmax = 3.06 Vp, 3.57 Vp, 4.08 Vp, and
4.59 Vp.
Vmax
Res
Qe
3.06
0.024
0.012
3.57
0.028
0.014
4.08
0.032
0.016
4.59
0.036
0.018
10-24. For the 12-bit linear PCM codes given, determine the voltage range that would be
converted to them:
12-Bit Linear Code
Resolution (V)
Range
10-26.
100011110010
0.12
29.04 V ±60 mV
000001000000
0.10
6.4 V ±50 mV
000111111000
0.14
7.056 V ±70 mV
111111110000
0.12
243.84 V ±60 mV
For the following eight-bit compressed codes, determine the expanded 12-bit code.
Eight-Bit Code
Twelve-Bit Code
11001010
100011010100
00010010
000000010010
10101010
100000110101
01010101
000101011000
11110000
110000100000
11011011
100110111000