A two stage receiving system operates at 30 MHz bandwidth. Calculate noise figure (F) of the system for following values of G1 (dB) and arrange them in ascending order. Assuming F1 (dB) = 2 dB, F2 (dB) = 9 dB A. G1 = 10 dB B. G1 = 20 dB C. G1 = 50 dB D. G1 = 30 dB E. G1 = 40 dB Choose the correct answer from the options given below :
\(C \lt E \lt D \lt B \lt A\)
The tool — Friis' formula for cascaded stages.
\(F=F_1+\dfrac{F_2-1}{G_1}\)
with every quantity in linear (ratio) form, not dB. The formula shows that the first stage's noise figure adds in full, while the second stage's excess noise is divided down by the gain that precedes it.
Step 1 — convert the dB data to ratios.
\(F_1=10^{2/10}=1.585, \qquad F_2=10^{9/10}=7.94 \Rightarrow F_2-1=6.94\)
Step 2 — evaluate F for each first-stage gain.
| Item | G1 (dB) | G1 (ratio) | F = 1.585 + 6.94/G1 | F (dB) |
|---|---|---|---|---|
| C | 50 | 105 | 1.5851 — smallest | 2.00 |
| E | 40 | 104 | 1.5857 | 2.00 |
| D | 30 | 1000 | 1.592 | 2.02 |
| B | 20 | 100 | 1.654 | 2.19 |
| A | 10 | 10 | 2.279 — largest | 3.58 |
Step 3 — read the ascending order. F falls monotonically as G1 rises, so ascending F is descending G1:
\(C \lt E \lt D \lt B \lt A\)
The design lesson. This is the single most important result in receiver design: the first stage dominates the noise performance of the whole chain. Give the front end enough gain (and the lowest possible F) and every later stage's noise becomes negligible — which is why a low-noise amplifier is placed first, ideally right at the antenna, and why any lossy component ahead of it (a long cable, a filter) directly degrades the system noise figure.
Note. The 30 MHz bandwidth is not needed for the ordering; it would only be used to compute absolute noise power, \(N=FkT_0B\).
Hence, the ascending order of noise figure is \(C \lt E \lt D \lt B \lt A\).
Similar Questions
Which of the following are useful in comparing the noise performance of receivers ?
1. Input noise voltage
2. Equivalent noise resistance
3. Noise temperature
4. Noise figureSelect the correct answer.
The minimum receivable signal in a radar receiver which has an IF bandwidth of 2.5 MHz and a 9-dB noise figure is : (Take T as 290° K)
Read the following statements.
(a) Industrial noise is usually of impulse type.
(b) HF mixers are generally noisier than HF amplifiers.
(c) Thermal noise is independent of frequency at which it is measured.
(d) Impulse noise voltage is independent of the bandwidth.
Which of the above statements are correct ?
Assertion (A) : Noise figure is defined as the ratio of the signal to noise power at the input terminal to the signal to noise power at the output terminal of the system.
Reason (R) : The noise figure will be less than 1 for an ideal receiver, which introduces no noise of its own.
Select your answer using the codes given below :
A mixer stage has a noise figure of 20 dB and is preceded by an amplifier that has a noise figure of 9 dB and an available power gain of 15 dB. The overall noise figure is :
List – I List – II a. Shot Noise i. Resistance b. Johnson Noise ii. Diode c. Current Noise iii. P-N junction d. Partition Noise iv. Triode Codes :
Important Questions from Noise Temperature and Noise Figure
Which of the following is not a primary source of external noise?
If each stage had a gain of 10 dB, and Noise Figure of 10 dB, then the overall Noise figure of a two-stage cascade amplifier will be
An antenna pointing in a certain direction has a noise temperature of 50 K. The ambient temperature is 290 K. The antenna is connected to a pre-amplifier that has a noise figure of 2 dB and an available gain of 40 dB over an effective bandwidth of 12 MHz. The effective input noise temperature Te for the amplifier and the noise power Pao at the output of the preamplifier, respectively, are
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Which of the following are useful in comparing the noise performance of receivers ?
1. Input noise voltage
2. Equivalent noise resistance
3. Noise temperature
4. Noise figureSelect the correct answer.
