ASU IFT 372 Fall 2023 Helm Weeks 1-7
Quizzes + Midterm Multisource with
complete solution
What is a logarithm?
Correct answer: A logarithm is an exponent based mathematical representation of a numerical value.
What logarithmic base is used in digital communications?
Correct answer: Two
How do you find a log2 value on a calculator that only has log10 functionality? (Hint: what is the
formula?)
Correct answer: log2(a) = [log10(a) / log10(2)]
What is the definition of a decibel?
Correct answer: a = 10lob(b), where a is the decibel value and b is the decimal value
Correct answer: A decibel is a mathematical representation of a power level on a logarithmic scale.
You cannot mix decimal and decibel values in an equation (i.e., you either have to work with decimal
values or decibel values)
Correct answer: True
There can be more than one power value in a decibel (dB) equation.
Correct answer: False
When you add two decibel values, you are multiplying those values in decimal (I.e. 3 dB + 6 dB = 9 dB
which is equivalent to 2 * 4 = 8 in decimal)
Correct answer: True
is a decibel value referenced to watts and is a decibel value referenced to milliwatts.
Correct answer: dBW & dBm
How do you convert dBW to dBm?
Correct answer: Add 30 dB to dBW to obtain dBm value
The net gain or (loss) of a transmission system is a radio between the and
where the is the numerator and the
is the denominator.
Correct answer: Output power & Input power
What parameter of the intelligent signal causes or determines the instantaneous rate of carrier
frequency?
Correct answer: Amplitude of the modulating signal
What parameter of the intelligent signal causes frequency deviation of the carrier?
Correct answer: Amplitude of the modulating signal
,Determine the noise power (in dBm) at 27° C in a 500 kHz bandwidth.
,Correct answer: PN = 10 log (1.38*10^-23*(27+273)*500kHz)
= -146.8 dBw
=> -116.8 dBm
Determine the noise power (in dBm) at 27° C in a 20 MHz bandwidth system.
Correct answer: Pn=kTB; k=1.38*(10^-23)W°K-Hz; T(°K)=27°C+273=300°K;
B=20*10^6Hz
=10log(1.38*(10^-23)*300*20*10^6)
=10log(8.28*(10^-14))
=-130.82 dBW
=-130.82 dBW +30 dB
=-100.8 dBm
Determine the noise power (in dBm) at 27°C in a 20MHz bandwidth system.
Correct answer: Pn=kTB; k=1.38*10^-23W°K-Hz; T(°K)=27°C+273=300°K;
B=20*10^6Hz
=10log(1.38*10^-23*300*20*10^6)
=10log(8.28*10^-14)
=-130.82 dBW
=-130.82 dBW + 30dB = -100.8dBm
Determine the noise power (in dBM) at 27°C in a 20 MHz bandwidth system.
k = 1.38 * 10^-23
T = 27 + 273 = 300
B = 20 * 10^6
PN = 10log(kTB)
PN = 10log((1.38 * 10^-23)(300)(20 * 10^6))
= -130.819
= -130.82
= -130.82 + 30 dB
= -100.8 dBm
Determine the noise power (in dBm) at 23°C in a 500 kHz bandwidth.
k = 1.38 * 10^23
T = 27 + 273 = 300
B = 5e5
PN = 10log(kTB)
= 10log(1.38 * 10^23 * 300 * 5e5)
= -146.8
= -146.8 + 30 dB
= -116.8 dBm
In a data transmission system, the is the physical path between the transmitter and
receiver
Transmission path and channel
For a 12-bit linear sign-magnitude PCM code with a resolution of 0.02 V, determine the voltage range
that would be converted to the PCM code 110000000000
, Correct answer: 1024 * .02 => 20.47V to 20.49V
An FM signal has a deviation of 75 kHz and a modulating frequency of 15 kHz. The carrier frequency is
1600 MHz. Using Carson's rule, what is the required bandwidth for this system?
Correct answer: BSCR = 2 * (75kHz + 15kHz) = 180kHz
Which of the following are strengths of OFDM?
Correct answer: Frequency selective fading does not adversely affect all subcarriers & effectively uses the
wireless spectrum.
Given a three stage amplifier system with stage 1 having a gain of 16 dB and a NF=3.5 dB, Stage 2 gain of
19 dB and a NF = 4.8 dB, Stage 3 having a gain of 20 dB and a NF = 4.17 dB, calculate the system noise
figure.
Correct answer: 16 dB => 40;
3.5 dB => 2.24;
19 dB => 80;
4.8 dB => 3.02;
20 dB => 100;
6.2 dB => 4.17
F = 2.24 + ((3.02-1)/40) + ((4.17-1)/(40*80)) = 2.29 => 2.6 dB
Consider an OFDM implementation that uses 15 kHz subcarriers and use an OFDM symbol of 2048
subcarriers. The nominal cyclic prefix accounts for a 7% guard time. The extended cyclic prefix can use up
to 25%. 1600 subcarriers can be used for data transmission. The rest are needed for pilot and null
subcarriers. The transmission bandwidth is 25 MHz using 8 QAM modulation.
What is the data rate for the nominal CP?
Correct answer: R = 25MHz * (1600 / [2048 + 205])*5=88.8 Mbps
What is the effective Temperature (Te in °K) for a system with a 29 dB input SNR and a 23 dB output SNR?
Correct answer: Noise Factor (F) = 10^2.^2.3 => 4
Effective Temp (Te) = (F – 1) * 290
= (4 – 1) * 290
= 3 * 290
= 870
OR
F = (1 + Te/290)
4 = (1 + Te/290)
4 - 1 = Te/290
870°K = Te
What is the effective Temperature (Te in °K) for a system with a 28 dB input SNR and a 24 dB ouptut SNR?
F = (1 + Te/290)
NF = 4 dB
F = 2.5
Quizzes + Midterm Multisource with
complete solution
What is a logarithm?
Correct answer: A logarithm is an exponent based mathematical representation of a numerical value.
What logarithmic base is used in digital communications?
Correct answer: Two
How do you find a log2 value on a calculator that only has log10 functionality? (Hint: what is the
formula?)
Correct answer: log2(a) = [log10(a) / log10(2)]
What is the definition of a decibel?
Correct answer: a = 10lob(b), where a is the decibel value and b is the decimal value
Correct answer: A decibel is a mathematical representation of a power level on a logarithmic scale.
You cannot mix decimal and decibel values in an equation (i.e., you either have to work with decimal
values or decibel values)
Correct answer: True
There can be more than one power value in a decibel (dB) equation.
Correct answer: False
When you add two decibel values, you are multiplying those values in decimal (I.e. 3 dB + 6 dB = 9 dB
which is equivalent to 2 * 4 = 8 in decimal)
Correct answer: True
is a decibel value referenced to watts and is a decibel value referenced to milliwatts.
Correct answer: dBW & dBm
How do you convert dBW to dBm?
Correct answer: Add 30 dB to dBW to obtain dBm value
The net gain or (loss) of a transmission system is a radio between the and
where the is the numerator and the
is the denominator.
Correct answer: Output power & Input power
What parameter of the intelligent signal causes or determines the instantaneous rate of carrier
frequency?
Correct answer: Amplitude of the modulating signal
What parameter of the intelligent signal causes frequency deviation of the carrier?
Correct answer: Amplitude of the modulating signal
,Determine the noise power (in dBm) at 27° C in a 500 kHz bandwidth.
,Correct answer: PN = 10 log (1.38*10^-23*(27+273)*500kHz)
= -146.8 dBw
=> -116.8 dBm
Determine the noise power (in dBm) at 27° C in a 20 MHz bandwidth system.
Correct answer: Pn=kTB; k=1.38*(10^-23)W°K-Hz; T(°K)=27°C+273=300°K;
B=20*10^6Hz
=10log(1.38*(10^-23)*300*20*10^6)
=10log(8.28*(10^-14))
=-130.82 dBW
=-130.82 dBW +30 dB
=-100.8 dBm
Determine the noise power (in dBm) at 27°C in a 20MHz bandwidth system.
Correct answer: Pn=kTB; k=1.38*10^-23W°K-Hz; T(°K)=27°C+273=300°K;
B=20*10^6Hz
=10log(1.38*10^-23*300*20*10^6)
=10log(8.28*10^-14)
=-130.82 dBW
=-130.82 dBW + 30dB = -100.8dBm
Determine the noise power (in dBM) at 27°C in a 20 MHz bandwidth system.
k = 1.38 * 10^-23
T = 27 + 273 = 300
B = 20 * 10^6
PN = 10log(kTB)
PN = 10log((1.38 * 10^-23)(300)(20 * 10^6))
= -130.819
= -130.82
= -130.82 + 30 dB
= -100.8 dBm
Determine the noise power (in dBm) at 23°C in a 500 kHz bandwidth.
k = 1.38 * 10^23
T = 27 + 273 = 300
B = 5e5
PN = 10log(kTB)
= 10log(1.38 * 10^23 * 300 * 5e5)
= -146.8
= -146.8 + 30 dB
= -116.8 dBm
In a data transmission system, the is the physical path between the transmitter and
receiver
Transmission path and channel
For a 12-bit linear sign-magnitude PCM code with a resolution of 0.02 V, determine the voltage range
that would be converted to the PCM code 110000000000
, Correct answer: 1024 * .02 => 20.47V to 20.49V
An FM signal has a deviation of 75 kHz and a modulating frequency of 15 kHz. The carrier frequency is
1600 MHz. Using Carson's rule, what is the required bandwidth for this system?
Correct answer: BSCR = 2 * (75kHz + 15kHz) = 180kHz
Which of the following are strengths of OFDM?
Correct answer: Frequency selective fading does not adversely affect all subcarriers & effectively uses the
wireless spectrum.
Given a three stage amplifier system with stage 1 having a gain of 16 dB and a NF=3.5 dB, Stage 2 gain of
19 dB and a NF = 4.8 dB, Stage 3 having a gain of 20 dB and a NF = 4.17 dB, calculate the system noise
figure.
Correct answer: 16 dB => 40;
3.5 dB => 2.24;
19 dB => 80;
4.8 dB => 3.02;
20 dB => 100;
6.2 dB => 4.17
F = 2.24 + ((3.02-1)/40) + ((4.17-1)/(40*80)) = 2.29 => 2.6 dB
Consider an OFDM implementation that uses 15 kHz subcarriers and use an OFDM symbol of 2048
subcarriers. The nominal cyclic prefix accounts for a 7% guard time. The extended cyclic prefix can use up
to 25%. 1600 subcarriers can be used for data transmission. The rest are needed for pilot and null
subcarriers. The transmission bandwidth is 25 MHz using 8 QAM modulation.
What is the data rate for the nominal CP?
Correct answer: R = 25MHz * (1600 / [2048 + 205])*5=88.8 Mbps
What is the effective Temperature (Te in °K) for a system with a 29 dB input SNR and a 23 dB output SNR?
Correct answer: Noise Factor (F) = 10^2.^2.3 => 4
Effective Temp (Te) = (F – 1) * 290
= (4 – 1) * 290
= 3 * 290
= 870
OR
F = (1 + Te/290)
4 = (1 + Te/290)
4 - 1 = Te/290
870°K = Te
What is the effective Temperature (Te in °K) for a system with a 28 dB input SNR and a 24 dB ouptut SNR?
F = (1 + Te/290)
NF = 4 dB
F = 2.5
