Noise and SNR Interview Questions

Q1. What is thermal noise and what determines its power?

Thermal noise is random voltage fluctuations generated by the thermal agitation of charge carriers in any resistor, and its power is given by P = kTB, where k is Boltzmann's constant, T is temperature in Kelvin, and B is bandwidth in Hz. A 50-ohm resistor at 290 K over a 1 MHz bandwidth produces about -114 dBm of noise power. This sets the absolute floor below which no signal can be detected regardless of how good the amplifier is.

Follow-up: Why does increasing bandwidth increase noise power even though you are not adding any components?

Q2. What is SNR and how is it calculated?

SNR is the ratio of signal power to noise power at a specific point in the system, expressed in dB as 10 log10(Psignal / Pnoise). An FM receiver with a 1 µV signal into a 50-ohm input and -120 dBm noise floor has an SNR of about 26 dB. SNR must always be referenced to a specific point because it changes at every amplifier, filter, and cable in the chain.

Follow-up: At what SNR does a BPSK system achieve a BER of 10^-5?

Q3. What is noise figure and how does it relate to noise temperature?

Noise figure (NF) is the degradation in SNR caused by a component, expressed in dB as 10 log10(SNRin / SNRout), and noise temperature Te relates to it by Te = T0(F-1) where T0 is 290 K. An LNA with a 1 dB noise figure has an equivalent noise temperature of about 75 K added to the input. Noise figure is used at room temperature systems while noise temperature is preferred in satellite and radio astronomy receivers where sub-Kelvin resolution matters.

Follow-up: How does the noise figure of a cascade of stages depend on gain?

Q4. State the Friis noise figure formula and explain what it tells you.

The Friis formula states that the total noise figure of a cascade is F_total = F1 + (F2-1)/G1 + (F3-1)/(G1*G2) + ..., where F and G are linear noise figure and gain of each stage. In a satellite receiver, if the first LNA has 2 dB NF and 20 dB gain, the second mixer's 8 dB NF contributes only 0.06 dB to the total. This proves that the first stage dominates overall system noise, which is why LNA design is the highest-priority task in any receiver chain.

Follow-up: What happens to total system noise figure if the first stage is a lossy component like a cable?

Q5. What is the difference between SNR and SINAD?

SNR measures signal power relative to noise only, while SINAD (Signal to Noise and Distortion) includes harmonic distortion products in the denominator, making it a more complete measure of ADC and receiver quality. A 12-bit ADC may show 74 dB theoretical SNR but only 70 dB SINAD because third-harmonic distortion consumes 4 dB of dynamic range. In practice SINAD is more useful for ADC datasheets because distortion in real converters often dominates noise at high signal amplitudes.

Follow-up: How is ENOB related to SINAD?

Q6. What is shot noise and in what devices is it dominant?

Shot noise arises from the discrete nature of electric charge and appears whenever current crosses a potential barrier, with spectral density 2qI where q is electron charge and I is DC current. In a photodiode receiving 1 µA of photocurrent, the shot noise current spectral density is about 18 fA/√Hz, which limits the minimum detectable optical power. In resistors at low frequencies, thermal noise dominates, but shot noise becomes significant in p-n junctions, BJT base currents, and vacuum tubes.

Follow-up: Why does shot noise increase with DC bias current in a BJT?

Q7. What is flicker noise and what frequency range does it affect?

Flicker noise, also called 1/f noise, has a power spectral density that rises inversely with frequency and dominates below the corner frequency, which is typically between 1 kHz and 100 kHz depending on the device. In MOSFET op-amps like the TL071, flicker noise dominates below about 100 Hz, which is why JFET-input op-amps are preferred for audio preamp designs where low-frequency noise is critical. CMOS processes with smaller gate oxides generally have higher flicker noise corner frequencies than older processes.

Follow-up: How does chopper stabilization in amplifiers suppress the effect of flicker noise?

Q8. What is noise bandwidth and how does it differ from -3 dB bandwidth?

Noise bandwidth is the bandwidth of an ideal rectangular filter that passes the same total noise power as the actual filter, and it is always wider than the -3 dB bandwidth for real filters. A first-order RC filter with a 1 kHz -3 dB bandwidth has a noise bandwidth of π/2 × 1 kHz ≈ 1.571 kHz. Using -3 dB bandwidth in noise calculations underestimates total noise power, which causes measured noise floors to come out lower than actual values.

Follow-up: How does filter order affect the ratio of noise bandwidth to -3 dB bandwidth?

Q9. What is the noise floor of an ideal receiver at room temperature?

The noise floor of an ideal receiver at 290 K is -174 dBm/Hz, derived from kTB with B = 1 Hz. For a 10 MHz bandwidth receiver, the noise floor rises to -174 + 70 = -104 dBm before accounting for any component noise figure. Every real receiver adds its noise figure on top of this, so a 6 dB NF system has a -98 dBm noise floor at 10 MHz bandwidth.

Follow-up: Why is the reference temperature chosen as 290 K rather than 300 K?

Q10. How does antenna temperature contribute to receiver system noise?

Antenna temperature is the equivalent noise temperature corresponding to the noise power received from the environment, including ground thermal radiation, atmospheric absorption, and cosmic background radiation. A ground-pointing antenna at 10 GHz may see 300 K antenna temperature, while a zenith-pointing dish sees only 20-30 K because cold sky is in the beam. In satellite ground stations, antenna temperature often dominates the noise budget, not the receiver itself.

Follow-up: What is G/T and why is it used as a figure of merit for satellite earth stations?

Q11. What effect does attenuation before an LNA have on system noise figure?

Any lossy element before the LNA — such as a transmission line, filter, or switch — adds noise equal to its physical temperature multiplied by its loss factor and directly degrades the system noise figure by its loss in dB. A 3 dB cable loss before the LNA raises the system noise floor by 3 dB, making it equivalent to halving the antenna aperture. This is why satellite receivers, radio telescopes, and cellular base station towers mount the LNA directly at the antenna feed rather than at the end of a long coax run.

Follow-up: How does cryogenic cooling of a low-noise amplifier improve system sensitivity?

Q12. What is the relationship between SNR and bit error rate in digital communication?

In BPSK, the BER is Q(√(2Eb/N0)) where Eb/N0 is the energy per bit to noise spectral density ratio, and Q is the complementary error function integral. At Eb/N0 = 10.5 dB, BPSK achieves BER = 10^-6, while QPSK requires the same Eb/N0 for the same BER but transmits twice the data rate. The relationship is not linear — a 3 dB improvement in Eb/N0 near the waterfall region can reduce BER by multiple orders of magnitude.

Follow-up: Why does 16-QAM require a higher Eb/N0 than QPSK for the same BER?

Q13. What is inter-modulation distortion and how does it degrade SNR?

Intermodulation distortion (IMD) occurs when two or more signals mix through a nonlinear device and produce spurious products at sum and difference frequencies, with third-order products landing closest to the original signals and being hardest to filter. In an RF amplifier with two tones at 100 MHz and 101 MHz, third-order IMD products appear at 99 MHz and 102 MHz, directly in the receive band. The third-order intercept point (IP3) characterizes this: an LNA with +10 dBm IIP3 has a dynamic range floor set by third-order IMD for strong adjacent-channel signals.

Follow-up: What is the relationship between IIP3 and the 1 dB compression point?

Q14. What is dynamic range in a receiver?

Dynamic range is the range of input signal levels over which a receiver operates correctly, bounded at the bottom by the noise floor and at the top by compression or intermodulation distortion. A typical cellular receiver has a noise floor of -110 dBm and a 1 dB compression point of -20 dBm, giving about 90 dB of instantaneous dynamic range. Spurious-free dynamic range (SFDR) is a tighter bound defined by where the third-order IMD products rise above the noise floor.

Follow-up: How does automatic gain control extend the effective dynamic range of a receiver?

Q15. How does bandwidth affect the trade-off between SNR and data rate?

Shannon's theorem states that channel capacity C = B log2(1 + SNR), so doubling bandwidth doubles capacity but increasing SNR by 3 dB adds less capacity because the log relationship compresses the SNR gain. In a cable modem system, the noise floor rises by 3 dB when bandwidth doubles, so SNR drops by 3 dB even as capacity attempts to increase. At high SNR the log term grows slowly, meaning bandwidth is more valuable than SNR improvement; at low SNR the trade-off reverses.

Follow-up: Why do spread spectrum systems accept lower SNR per Hz in exchange for more bandwidth?