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)
6.946 × 10–14 W
The receiver's own noise, referred to its input, is what sets the minimum receivable signal — and it is computed from the effective noise temperature.
Step 1 — convert the noise figure to a ratio.
\(F=10^{9/10}=10^{0.9}=7.943\)
Step 2 — find the effective noise temperature. A noise figure states how much noise the receiver adds beyond that of a matched source at 290 K, so the excess corresponds to
\(T_{e}=\left(F-1\right)T_{0}=\left(7.943-1\right)\times290=6.943\times290=2013\ \text{K}\)
Step 3 — the noise power in the IF bandwidth.
\(S_{min}=kT_{e}B=1.38\times10^{-23}\times2013\times2.5\times10^{6}\)
\(=6.946\times10^{-14}\ \text{W}\)
— option 2.
The same figure written another way, which is how it is often computed:
\(kT_{0}B=1.38\times10^{-23}\times290\times2.5\times10^{6}=1.0005\times10^{-14}\ \text{W}\)
\(S_{min}=kT_{0}B\left(F-1\right)=1.0005\times10^{-14}\times6.943=6.946\times10^{-14}\ \text{W}\)
A note on the convention, since it decides the answer. Some texts define the minimum detectable signal as \(kT_{0}BF\), which would give \(7.95\times10^{-14}\) W — the total noise including the source's own contribution. That value is not among the options. The form used here, \(kT_{0}B(F-1)\), counts only the noise the receiver itself adds, and it is this excess-noise convention that the paper follows.
Why the answer matters in radar. The minimum receivable signal enters the range equation directly:
\(R_{max}=\left[\dfrac{P_{t}G^{2}\lambda^{2}\sigma}{\left(4\pi\right)^{3}S_{min}}\right]^{1/4}\)
Note the fourth root: halving \(S_{min}\) extends the range by only 19 %. That is why a 1 dB improvement in noise figure is prized — and why bandwidth is kept no wider than the pulse requires, since every extra hertz admits more noise for no extra signal.
Hence, the minimum receivable signal is 6.946 × 10−14 W.
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.
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 :
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
The noise figure of an amplifier is 3 dB. Its noise temperature will be about
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.
