Question 1:

Determine the following for the fixed-bias configuration

Question 2
For the given circuit please find:

Add a load of 4.5 kΩ and a source resistance of 0.3 kΩ, and determine the following

and compare to the no-load values (with 𝑟𝑜 = ∞Ω).

1e. Find load voltage gain 𝐴𝑣𝐿 .

1f. Calculate the output and input impedance 𝑍𝑜 and 𝑍𝑖 .

1e)
𝑅𝐿 ||𝑅𝐶
𝐴𝑉𝐿 = − = 139.226
𝑟𝑒
1f)

𝑍𝑖 = 𝑅1 ||𝑅2 ||𝛽𝑟𝑒

𝑍𝑖 = 56 × 103 ||8.2 × 103 ||1750.5 = 1.406 𝐾Ω

The input impedance of loaded and unloaded transistors is the same

𝑍𝑜 = 𝑅𝐶 = 6.8 𝑘Ω
Question 3:
If the circuit of Fig. has R1 = 100 kΩ and Rf = 500 k Ω, what output voltage results for an input of V1
= 2 V?
Question 4:
Calculate the output voltage of a noninverting amplifier (as in Fig.) for values of V1 = 2 V, Rf = 500 k
Ω, and R1 = 100 k Ω.
Question 5:
Calculate the output voltage of an op-amp summing amplifier for the following sets of voltages and
resistors. Use Rf = 1 M Ω in all cases.
Question 6:
(i). The input four-digit sequence waveforms are shown in
Figure b of the DAC in Figure a, where the input D0 is the LSB,
calculate
a. The input current of each weight,
b. Calculate the output voltage for continuous binary sequence
from 0000 to 1111 at the inputs,
c. Draw the output waveform of DAC in Figure 4.

Figure a. Four-bit DAC with binary-weighted inputs

Figure b. The input four-bit square waveforms.

(ii). Determine the resolution of the following DACs, expressed by a percentage.

d. An eight-bit DAC
Q Solution:

a)
3
𝑉
𝑖𝑓 = 3 ∑ 𝐷𝑖 2𝑖
2 𝑅
𝑖=0
For 𝑖 = 0
𝑉 0
5
𝑖𝑓 = 𝐷0 2 = 𝐷 × 1 = 3.125𝐷0 𝜇𝐴
23 𝑅 8 × 200 × 103 0
For 𝑖 = 1
𝑉 5
𝑖𝑓 = 𝐷1 21 = 𝐷 × 2 = 12.5𝐷1 𝜇𝐴
3
2 𝑅 8 × 100 × 103 1
For 𝑖 = 2
𝑉 5
𝑖𝑓 = 𝐷2 22 = 𝐷 × 4 = 50𝐷2 𝜇𝐴
3
2 𝑅 8 × 50 × 103 2
For 𝑖 = 3
𝑉 5
𝑖𝑓 = 𝐷3 23 = 𝐷 × 8 = 0.2𝐷3 𝑚𝐴
3
2 𝑅 8 × 25 × 103 3
b)

3 3
𝑉𝑅𝑓
𝑉𝑜𝑢𝑡 = −𝑖𝑓 𝑅𝑓 = 3 ∑ 𝐷𝑖 2𝑖 = −0.25 ∑ 𝐷𝑖 2𝑖
2 𝑅
𝑖=0 𝑖=0

The first input code is 0000; the corresponding output voltage is 0 V.

The second input code is 0001; the corresponding output voltage is −0.25 V.

The third input code is 0010; the corresponding output voltage is −0.5 V.

Then the input code becomes 0011; the corresponding output voltage is −0.75 V.

The output of each adjacent binary code is increased by −0.25 V for this continuous binary
sequence from 0000 to 1111 at the inputs; the output is a stair waveform from 0 to −3.75 V with a
stair step of −0.25 V. The basic quantitative unit is –0.25 V.

The output voltage is the product of digital quantity and basic quantitative unit.

c)
d)
1 1
𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 = × 100 = × 100 = 0.39%
2𝑛 − 1 28 − 1
Question 7:
Determine the binary code output of the three-bit flash ADC with uniform quantization
level for the input signal and conversion clock pulse as shown in Figure below.
Assume the reference voltage VREF = +8V. [15 marks]

Figure . Sampling of values on a waveform for converting to binary code

(ii). Determine the resolution of the following DACs, expressed by a percentage.

a. A four-bit DAC
b. An eight-bit DAC

(i)

Since the input analog signal is between 0 and 8 V and the three-bit code has eight states, eight
uniform quantisation level is 0 V, 1 V, 2 V, 3 V, 4 V, 5 V, 6 V, and 7 V, which correspond to eight
voltage region, that is, [0 V, 1 V], (1 V, 2 V], (2 V, 3 V], (3 V, 4 V], (4 V, 5 V], (5 V, 6 V], (6 V, 7 V], and
(7 V, 8 V].

Each voltage region has a unique binary code. Therefore, the resulting binary code sequence is
listed as follows and the corresponding waveforms are shown in Figure below associated with
the clock pulse.

100,110,111,110,100,010,000,001,011,101,110,111
(ii)

3a)
1 1
𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 = = 4 × 100% = 6.6%
2𝑛 −1 2 −1
3b)
1 1
𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 = = 8 × 100% = 0.39%
2𝑛 −1 2 −1
Operational Amplifiers:
𝑅
Non-Inverting amplifier: 𝑉𝑜 = (1 + 𝑅𝑓) 𝑉1
1

𝑅
Inverting amplifier: 𝑉𝑜 = − 𝑅𝑓 𝑉1
1

Unity follower amplifier: 𝑉𝑜 = 𝑉1

𝑅 𝑅 𝑅
Summing amplifiers: 𝑉𝑜 = − (𝑅𝑓 𝑉1 + 𝑅𝑓 𝑉2 + 𝑅𝑓 𝑉3 )
1 2 3

Digital-to-Analog Converter (DAC):

𝑉
the current through the feedback resistor Rf: 𝑖𝑓 = 23 𝑅 ∑3𝑖=0 𝐷𝑖 2𝑖

The output voltage: 𝑉𝑜 = −𝑖𝑓 𝑅𝑓

1
Resolution: Resolution= 2𝑛 −1