EXAM 1 Solution
 Problem 1 (20 points):
 #Q1. (3 points) A 14-bit analog-to-digital converter (ADC) has an input range of 1V to 6 V. If the output
 of the ADC is 74, what is the voltage at its input? Ignore quantization error.
 
 #Q1. (3 points) A 12-bit analog-to-digital converter (ADC) has an input range of 2V to 5 V. If the output
 of the ADC is 47, what is the voltage at its input? Ignore quantization error.
 
 #Q2. (3 points) Briefly state the purpose of using voltage followers.
 Used as a buffer between two stages since it has infinite input impedance and zero output impedance.
 #Q3. (3 points) An analog signal contains three sinusoidal components with frequencies 5, 7 and 12 Hz.
 What is the minimum sampling rate required in order to avoid aliasing?
 24 sps
 #Q3. (3 points) An analog signal contains three sinusoidal components with frequencies 5, 7 and 24 Hz.
 What is the minimum sampling rate required in order to avoid aliasing?
 48 SPS
2
#Q4. (3 points) A6-bit ADC has an input range of 1 to 4.15 V. If the analog input changes by 82 mV over
 two samples (which are between 2 to 3V), the estimated voltage after ADC will change by (circle one)

 #Q4. (3 points) A6-bit ADC has an input range of 1 to 4.15 V. If the analog input changes by 108 mV over
 two samples (which are between 2 to 3V), the estimated voltage after ADC will change by (circle one)

 #Q5. (2 points) How many comparators are required to build a 3-bit direct conversion analog-to-digital
 converter (ADC)? (circle one)
3 4 5 7 8
 9 15 16 17 31
 #Q5. (2 points) How many comparators are required to build a 4-bit direct conversion analog-to-digital
 converter (ADC)? (circle one)

 #Q6. (2 points) For a given input signal, if the sampling rate of an ADC is increased, the signal-toquantization-noise ratio (SQNR)(circle one)
a) must increase
 b) must decrease
 c) may or may not change
 d) will not change
 #Q7. (4 points) A 10 Hz signal accompanied by a 60 Hz noise is passed through a filter with the transfer
 function,
 
 The signal-to-noise ratio (SNR) at the output of the filter is 54 dB. Find the SNR in dB at the input of the
 filter.
 Input SNR+ SNR gain at filter=Output SNR
 
 Problem 2 (35 points): Answer any five; 7 points each
# P2.1:The two filters shown below have transfer functions H1(s) and H2(s). Their input impedances are
15 kΩ and 10 kΩ, respectively, while their output impedances are 2 kΩ and 3 kΩ, respectively. The
output of the second filter is connected to a voltage divider as shown. Find Hac(s), the transfer function
of the entire system.

# P2.2:A sinusoidal voltage with frequency,? Hz, is sampled using an ADC at a constant sampling rate.
The first 10 samples of the digitized signal are shown above. Ignore any quantization error. Which of the
following are some possible values of ?(circle all that apply) ?
 2 3 4 5 6 7 8
 # P2.2: A sinusoidal voltage with frequency,? Hz, is sampled using an ADC at a constant sampling rate.
 The first 13samples of the digitized signal are shown above. Ignore any quantization error. Which of the
 following are some possible values of ?(circle all that apply) ?
 5
 P2.3:What is the root mean square (rms) value of the periodic voltage waveform shown below?

# P2.3:What is the root mean square (rms) value of the periodic voltage waveform shown below?
6
# P2.4:In the circuit shown below, ??? and ???? are the input and output voltages, respectively. Find

#P2.5: In the instrumentation amplifier (IA) shown below, 5?1 = ?2 . The common-mode and
 difference mode gains of the second stage
 are 0.01 and 10, respectively.
 
 
 P2.5: In the instrumentation amplifier (IA) shown below, 5?1 = ?2. The common-mode and difference
 mode gains of the second stage are 0.1 and
 10, respectively.
 c) [5 points] What is the common
 mode rejection ratio (CMRR) of the
 entire IA?
 d) [2 points] The difference mode
 component of the input is the
 desired signal while the common
 mode component is considered
 noise. If the input signal-to-noise
 ratio (SNR) = -46 dB, what is the
 SNR at the output of the IA?
 
 # P2.6: A bioelectric signal fluctuates between 2 V and 3 V (it can be modeled as a uniformly
 distributed random variable within this range). It is sampled using two different ADCs without any
 amplification:
 (a) 5-bit ADC with an input range of 2V to 3V
 (b) 7-bit ADC with an input range of 2V to 4V
 Find the signal-to-quantization-noise ratio (SQNR) for each of these ADCs.
 # P2.6: A bioelectric signal fluctuates between 2 V and 3 V (it can be modeled as a uniformly
 distributed random variable within this range). It is sampled using two different ADCs without any
 amplification:
 (c) 5-bit ADC with an input range of 0V to 3V
 (d) 7-bit ADC with an input range of 2V to 3V
 Find the signal-to-quantization-noise ratio (SQNR) for each of these ADCs.
 
 Problem 3 (45 points): Answer any three; 15 points each
# P3.1:You want to amplify (with or without inversion) an EKG signal that has arange from -20 mV
to+60mV. Design a dc-coupled one-op-amp amplifier circuit that will have the maximal gain possible
without exceeding the typical guaranteed linear output range (bounded by the op amp’s supply voltages
+10V and -10V). You can choose resistors of any values you want. If you need an additional voltage
source, use 10V or -10V. Clearly draw your amplifier circuit and calculate the required values.

summing amp
# P3.1: You want to amplify (with or without inversion) an EKG signal that has a range from -30 mV
 to+70mV. Design a dc-coupled one-op-amp amplifier circuit that will have the maximal gain possible
 without exceeding the typical guaranteed linear output range (bounded by the op amp’s supply voltages
 +10V and -10V). You can choose resistors of any values you want. If you need an additional voltage
 source, use 10V or -10V. Clearly draw your amplifier circuit and calculate the required values.
 
 # P3.2:In the difference amplifier circuit shown below, the op amp is ideal.
(a) (3 points) If the resistors are all 1 kΩ each:
 
 (b) (12 points) When the resistors are not equal, let ???? = 5?? - 4??. Find the CMRR of the difference
 amplifier.
 
 # P3.2: In the difference amplifier circuit shown below, the op amp is ideal.
 (c) (3 points) If the resistors are all 2 kΩ each:
 · Input impedance of the circuit as seen by
 the source, ?? = 2KΩ
 · Input impedance of the circuit as seen by
 the source, ?? = 4KΩ
 · Common mode rejection ratio (CMRR) of
 the circuit =∞
 (d) (12 points) When the resistors are not equal, let ???? = 4?? - 5??. Find the CMRR of the difference
 
 # P3.3: A biopotential voltage, ??? , is applied to the input of the circuit shown below. The output of
 the circuit, ??,is connected to the input of an 8-bit analog-to-digital converter (ADC). The ADC has an
 input range of 1 V to 5 V. The raw output of the ADC, denoted as ?, is an integer between 0 and ?.
 Ignore any quantization error.
 a) (3 points) Find the valueof?.(2)8 -1= 255
 b) (12 points) Find the value of ??? when ? = 100.
 A biopotential voltage, ??? , is applied to the input of the circuit shown below. The output of
 the circuit, ??, is connected to the input of an ?-bit analog-to-digital converter (ADC). The ADC has an
 input range of 1 V to 3 V. The raw output of the ADC, denoted as ?, is an integer between 0 and 511.
 Ignore any quantization error.
 a) (3 points) Find the value ?.
 b) (12 points) Find the value of ??? when ? = 150.
 The analog biopotential signal, ?(?), shown below is sampled using an?-bit direct conversion
analog-to-digital converter (ADC) starting at time ? = 0. The digitized values (???? ) are shown for ? = 0
 to 6, where ? is the sample index. The ADC has uniform quantization.
 (a) (3 points) What is the sampling rate? 2 sps
(b) (3 points) Find ?, the voltage resolution of the ADC.0.5 V
(c) (3 points) What is the minimum possible value of?? 3
(d) (3 points) What is the maximum magnitude of quantization error in this graph? For which
 sample?n=4 error=0.22 or, n=5 error=0.2
(e) (3 points) Instead of?(?), if you sample 2?(?) using this ADC, the value of???? (0) will be 2. What
 
 Bonus Problem (10 points):
 #B1:(3 points)Forthe instrumentation amplifier circuit in Problem P2.5, let ?1 = ?2 + 0.5 = 2 V and
5?1 = ?2 = 5 kΩ. Find the voltage at the output of the top left op amp.
+4.5 V
#B1:(3 points)For the instrumentation amplifier circuit in Problem P2.5, let ?1 = ?2 - 0.5 = 2 V and

 #B2:(2 points)When a voltage source ?? (with no source resistance) is connected to the input of a
certain amplifier circuit, the current leaving the source is, ? = 2??-3
6
, where ? and ?? are in Amperes and
Volts, respectively. What is the input impedance of the amplifier circuit?

#B2:(2 points)When a voltage source ?? (with no source resistance) is connected to the input of a
certain amplifier circuit, the current leaving the source is, ? = 3??-2
6
, where ? and ?? are in Amperes and
Volts, respectively. What is the input impedance of the amplifier circuit?
???
?? = 2 Ω
16
#B3: (5 points)A voltmeter has an input resistance of 18 kΩ. If it is connected between points ‘a’ and ‘b’
in the circuit shown below, what voltage will it read?
 #B3: (5 points)A voltmeter has an input resistance of 12 kΩ. If it is connected between points ‘a’ and ‘b’
in the circuit shown below, what voltage will it read?