Receiver Parameters

A radio receiver must perform three fundamental tasks with precision: detect very weak signals buried in noise, reject unwanted signals at adjacent or nearby frequencies, and reproduce the original message with acceptable distortion. The three parameters that quantify how well a receiver accomplishes these tasks are sensitivity, selectivity, and fidelity. These parameters form the basis for receiver specification sheets and are directly tested in GATE and competitive examinations.

Sensitivity

The sensitivity of a receiver is defined as the minimum input signal power required to produce a specified output signal quality, typically expressed as a minimum acceptable output SNR (for analog receivers) or a minimum bit error rate (for digital receivers). It is measured in dBm (decibels relative to 1 milliwatt). A highly sensitive receiver can detect very weak signals. Sensitivity is fundamentally limited by the internal noise generated in the receiver, particularly in the first amplification stage.

The minimum detectable signal (MDS) relates directly to the receiver noise figure F and bandwidth B. The available thermal noise power at the input from a matched source at 290 K is N_in = k T_0 B = -174 dBm/Hz + 10 log B. The MDS is then: MDS (dBm) = -174 + 10 log B + NF + SNR_min, where NF is the noise figure in dB and SNR_min is the minimum required output SNR in dB. Reducing noise figure directly improves sensitivity on a one-for-one dB basis.

In a superhet receiver, the image frequency is a spurious input frequency that also mixes to the same intermediate frequency as the desired signal. Image rejection is a sensitivity-related specification: if the image is not adequately rejected by the RF filter before the mixer, a strong image signal can raise the effective noise floor and degrade sensitivity for the desired channel.

Selectivity

The selectivity of a receiver quantifies its ability to separate the desired signal from undesired signals on adjacent or nearby frequencies. In a superheterodyne receiver, selectivity is primarily determined by the IF (intermediate frequency) bandpass filter. A selective receiver has a sharp filter response: high attenuation for frequencies outside the passband and flat response within the passband.

Selectivity is often characterized by the shape factor, defined as the ratio of the filter bandwidth at 60 dB attenuation to the bandwidth at 6 dB attenuation (or sometimes 60:3 dB). An ideal rectangular filter would have a shape factor of 1. Practical crystal, ceramic, or SAW filters may have shape factors of 1.5 to 3. The intermediate frequency itself affects selectivity: a higher IF makes the RF preselector filter easier to design for image rejection, but a lower IF allows sharper IF filter roll-off for better channel selectivity.

Fidelity

The fidelity of a receiver measures how accurately the output reproduces the original modulating signal. Fidelity is degraded by several mechanisms: insufficient bandwidth (cutting off high-frequency message components), amplitude nonlinearity (creating harmonic distortion), phase nonlinearity (causing phase distortion and inter-symbol interference in digital signals), and frequency response irregularities within the passband. Total harmonic distortion (THD) is a common fidelity metric for audio receivers.

Fidelity and selectivity are inherently in tension. Making the IF filter narrower improves selectivity but can cut into the signal sidebands, attenuating high-frequency message components and reducing fidelity. For AM broadcast receivers, the standard IF bandwidth is 10 kHz (allowing audio up to 4.5 kHz), which is a compromise between selectivity and fidelity. High-fidelity FM receivers use a wider IF bandwidth (180-200 kHz for beta = 5 with W = 15 kHz) to preserve the full audio spectrum.

The Superheterodyne Receiver and Parameter Balance

The superheterodyne receiver architecture was developed specifically to allow all three parameters to be optimized more or less independently. By converting the incoming RF signal to a fixed intermediate frequency using a local oscillator and mixer, the IF amplifier and filter can be designed once to have excellent selectivity and low noise at a fixed center frequency. Tuning is achieved by varying the local oscillator frequency while the IF chain remains unchanged. An automatic gain control (AGC) system maintains constant output level across a wide range of input signal strengths, effectively extending the receiver's dynamic range and preventing strong signals from saturating the output.

Numerical Example

A superhet AM receiver has a noise figure of 8 dB, an IF bandwidth of 10 kHz, and requires a minimum output SNR of 20 dB for acceptable demodulation. We calculate the minimum detectable signal (sensitivity) of this receiver.

Given:
Noise figure: NF = 8 dB
IF bandwidth: B = 10 kHz
Minimum output SNR: SNR_min = 20 dB
Thermal noise floor at 290 K: -174 dBm/Hz

Why this formula applies:
MDS accounts for thermal noise floor, bandwidth, receiver NF, and required SNR.

Formula:
MDS (dBm) = -174 + 10 log10(B) + NF + SNR_min

Substitution:
10 log10(10,000) = 10 × 4 = 40 dB
MDS = -174 + 40 + 8 + 20

Calculation:
MDS = -174 + 68

Final Answer: MDS = -106 dBm
Any input signal stronger than -106 dBm will produce at least 20 dB output SNR.
A lower NF or narrower bandwidth would improve (lower) the MDS.

Exam Tip: In GATE, sensitivity is always a minimum power level in dBm. Better sensitivity means a more negative dBm value (lower power threshold). The MDS formula MDS = -174 + 10 log B + NF + SNR_min is directly applicable. Every 1 dB reduction in NF improves sensitivity by exactly 1 dB. A common trap is confusing sensitivity (noise-limited minimum signal) with selectivity (adjacent channel rejection).

Mechanism: Superhet Receiver Parameter Flow

• Sensitivity: minimum input power for acceptable output quality. MDS = -174 + 10 log B + NF + SNR_min (all in dB/dBm).
• Better sensitivity means lower dBm value. Improved by reducing NF (LNA design) or reducing bandwidth.
• Selectivity: ability to reject adjacent channels. Determined by IF filter shape factor (BW_60dB / BW_6dB). Closer to 1 = better.
• Fidelity: accuracy of message reproduction. Quantified by THD, frequency flatness, and phase linearity in passband.
• Trade-off: narrower IF bandwidth improves selectivity but degrades fidelity. Wider bandwidth improves fidelity but reduces selectivity and sensitivity.
• Superhet architecture separates tuning (LO) from selectivity (fixed IF filter), allowing independent optimization of all three parameters.

Quick Revision

• Sensitivity = minimum detectable signal. MDS (dBm) = -174 + 10 log B + NF + SNR_min. Lower MDS = better.
• Every 1 dB NF improvement = 1 dB sensitivity improvement (direct linear relationship).
• Selectivity = adjacent channel rejection. Measured by IF filter shape factor = BW_60dB / BW_6dB. Ideal = 1.
• Fidelity = message reproduction accuracy. Degraded by insufficient bandwidth, nonlinearity, phase distortion.
• Selectivity vs fidelity: narrower filter is more selective but cuts sidebands, reducing fidelity.
• Superhet receiver: LO tunes the station, fixed IF filter provides selectivity, LNA sets sensitivity.
• Trap: sensitivity is a noise-limited concept (depends on NF and B), not a frequency-selectivity concept (that is selectivity).