Superheterodyne receivers

The superheterodyne translates every station to a fixed IF: mixing, LO injection, image frequency and rejection, IF choice, tracking and AGC.

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Why it matters

Almost every radio receiver built in the last ninety years — broadcast sets, spectrum analysers, radar receivers, telemetry ground stations — is a superheterodyne or a close descendant. Understanding it means understanding mixing, image frequencies and the selectivity–sensitivity trade-off, which also govern heterodyne optical detection and the front end of any instrument that measures RF signals.

Key ideas

The problem it solves. A tuned radio frequency (TRF) receiver must tune several high-Q stages together across the band, and its bandwidth changes as it tunes (B = f/Q). The superheterodyne instead translates every wanted station to one fixed intermediate frequency (IF), where fixed, high-gain, sharply selective filters and amplifiers do most of the work.

Block diagram. Antenna → RF stage (preselector: tuned circuit plus low-noise amplifier) → mixer → IF amplifier and filter → detector → audio/baseband amplifier. A local oscillator (LO) feeds the mixer and is ganged with the RF tuning so that the difference frequency always equals the IF. Automatic gain control (AGC) feeds a voltage derived from the detector back to the RF and IF stages to hold the output level steady while the received signal fades.

Mixing. A mixer is a non-linear device or a multiplier. Multiplying cos(2πf_s·t) by cos(2πf_LO·t) gives components at f_LO − f_s and f_LO + f_s; the IF filter keeps one of them, normally the difference. Mixing translates the spectrum without changing the modulation: AM stays AM, FM keeps its deviation.

High-side and low-side injection. With high-side injection f_LO = f_s + f_IF; with low-side f_LO = f_s − f_IF. Broadcast AM receivers use high-side injection because the required LO tuning ratio is smaller, so a practical ganged capacitor can cover it.

Image frequency. A second input frequency also produces the IF: the one on the other side of the LO. For high-side injection f_si = f_s + 2f_IF (for low-side, f_s − 2f_IF). Once an image reaches the mixer it cannot be separated from the wanted signal, so it must be rejected before the mixer by the preselector. The image-rejection ratio of a single tuned circuit of loaded quality factor Q is α = √(1 + Q²ρ²) with ρ = f_si/f_s − f_s/f_si. Cascaded tuned stages multiply their α values.

Choosing the IF. A high IF puts the image far away (easy image rejection) but makes narrow IF filtering harder and reduces adjacent-channel selectivity. A low IF gives excellent adjacent-channel selectivity but poor image rejection at high signal frequencies. Typical values: 455 kHz for AM broadcast, 10.7 MHz for FM broadcast, tens of MHz for TV and radar. Double-conversion receivers use a high first IF for image rejection and a low second IF for selectivity.

Figures of merit.

  • Sensitivity: the smallest input that gives a specified output SNR; set mainly by the noise figure and gain of the RF stage.
  • Selectivity: the ability to reject adjacent channels; set mainly by the IF filter shape.
  • Fidelity: how faithfully the full message bandwidth is reproduced.
  • Image rejection and IF rejection (rejecting signals at the IF itself, which leak through the mixer).
  • Tracking: the LO and RF tuned circuits must stay a constant IF apart across the band; padder and trimmer capacitors give exact tracking at three points.

Other spurious responses. Mixer non-linearity produces outputs at m·f_LO ± n·f_s; any combination that falls at the IF gives a spurious response. Double spotting (hearing a strong station at two dial settings) is the image problem seen from the user's side.

Formulas

f_IF = |f_LO − f_s| f_IF intermediate frequency, f_LO local oscillator frequency, f_s wanted signal frequency (all Hz).

f_LO = f_s + f_IF (high-side) ; f_LO = f_s − f_IF (low-side)

f_si = f_s + 2f_IF (high-side) ; f_si = f_s − 2f_IF (low-side) f_si image frequency (Hz).

ρ = f_si/f_s − f_s/f_si, α = √(1 + Q²ρ²) Q loaded quality factor of the preselector tuned circuit (dimensionless), α image-rejection ratio (dimensionless; 20·log₁₀α in dB). For n identical stages α_total = αⁿ.

C_max/C_min = (f_max/f_min)² Capacitance ratio needed to tune an LC circuit from f_min to f_max (L fixed).

Worked examples

Example 1 (standard). A medium-wave receiver with IF = 455 kHz and high-side injection is tuned to 1000 kHz. The preselector has Q = 100. Find f_LO, the image frequency and the image-rejection ratio.

  1. f_LO = f_s + f_IF = 1000 + 455 = 1455 kHz.
  2. f_si = f_s + 2f_IF = 1000 + 910 = 1910 kHz.
  3. ρ = 1910/1000 − 1000/1910 = 1.910 − 0.5236 = 1.386.
  4. α = √(1 + (100 × 1.386)²) = √(1 + 19 222) = 138.6, i.e. 20·log₁₀(138.6) = 42.8 dB. Answer: f_LO = 1455 kHz, f_si = 1910 kHz, α ≈ 139 (≈ 43 dB).

Example 2 (GATE level). The same receiver design (Q = 100, IF = 455 kHz) is used at f_s = 25 MHz. Find the image rejection, and then the rejection if the IF is raised to 10.7 MHz.

  1. IF 455 kHz: f_si = 25 + 0.91 = 25.91 MHz; ρ = 25.91/25 − 25/25.91 = 1.0364 − 0.9649 = 0.0715.
  2. α = √(1 + (100 × 0.0715)²) = √(1 + 51.15) = 7.22 → 17.2 dB.
  3. IF 10.7 MHz: f_si = 25 + 21.4 = 46.4 MHz; ρ = 46.4/25 − 25/46.4 = 1.856 − 0.5388 = 1.317.
  4. α = √(1 + (131.7)²) ≈ 131.7 → 42.4 dB. Answer: about 7.2 (17 dB) with a 455 kHz IF versus about 132 (42 dB) with a 10.7 MHz IF — the reason short-wave receivers use a high first IF.

Example 3 (tracking). An AM receiver covers 540–1650 kHz with IF 455 kHz and high-side injection. Compare the capacitance ratios needed for the RF and LO tuned circuits.

  1. RF: (1650/540)² = (3.056)² = 9.34.
  2. LO range: 540 + 455 = 995 kHz to 1650 + 455 = 2105 kHz; (2105/995)² = (2.116)² = 4.48. Answer: RF needs ≈ 9.3, LO needs ≈ 4.5. Low-side injection would need an LO from 85 to 1195 kHz, a ratio of about 198 — impractical, which is why high-side injection is used.

Common mistakes

  • Computing the image as f_LO + 2f_IF or f_s + f_IF. The image is 2f_IF away from the signal, mirrored about the LO.
  • Expecting the IF filter to reject the image. Image and wanted signal both become the IF; only filtering before the mixer helps.
  • Forgetting that selectivity (adjacent channel) and image rejection pull the IF choice in opposite directions.
  • Using unloaded Q for the preselector; the antenna and mixer load lower it.
  • Mixing up which stage sets sensitivity (RF front end, noise figure) and which sets selectivity (IF filter).

For GATE IN

  • Given f_s and f_IF, find f_LO and the image for high- or low-side injection; often an MCQ with both answers present, so read the injection side carefully.
  • Image-rejection ratio with a given Q, including cascaded stages and dB conversion.
  • LO tuning range and capacitance ratio questions.
  • Conceptual questions on AGC, double conversion, and why the IF value is chosen.

Quick check

  1. A receiver with IF 10.7 MHz and high-side LO is tuned to 98 MHz. What is the image frequency?
  2. Where in the receiver must the image be rejected?
  3. Two identical preselector stages each give α = 20. What is the total image rejection in dB?
  4. Which stage mainly sets adjacent-channel selectivity? Answers: 1. 119.4 MHz. 2. Before the mixer (RF stage). 3. 400, i.e. 52 dB. 4. The IF filter/amplifier.

Interview questions

All Communication and Optical Instrumentation interview questions

Try answering each one aloud before you open it.

  1. 1.What is a superheterodyne receiver?Concept

    A superheterodyne receiver is a type of radio receiver that uses frequency mixing to convert a received signal to a fixed intermediate frequency (IF), which can be more easily processed than the original carrier frequency. This design improves selectivity and sensitivity, making it the most common architecture for radio receivers.

  2. 2.Explain the role of the local oscillator in a superheterodyne receiver.Concept

    The local oscillator in a superheterodyne receiver generates a frequency that mixes with the incoming radio frequency (RF) signal to produce an intermediate frequency (IF). This mixing process is crucial because it allows the receiver to convert various incoming frequencies to a single IF, which simplifies filtering and amplification.

  3. 3.Why is an intermediate frequency (IF) used in superheterodyne receivers?Application

    An intermediate frequency (IF) is used in superheterodyne receivers to allow for easier and more effective filtering and amplification. By converting the received signal to a fixed IF, the receiver can use fixed-tuned filters and amplifiers, which are more efficient and cost-effective than variable-tuned components.

  4. 4.What happens if the local oscillator frequency is not stable in a superheterodyne receiver?Application

    If the local oscillator frequency is not stable, it can lead to drift in the intermediate frequency (IF), causing the receiver to lose the desired signal or pick up unwanted signals. This instability can degrade the performance of the receiver, affecting both selectivity and sensitivity.

  5. 5.How does image frequency affect a superheterodyne receiver, and how is it mitigated?Application

    The image is the second input frequency that mixes with the LO to give the IF: f_si = f_s + 2f_IF for high-side injection. Once it reaches the mixer it becomes indistinguishable from the wanted signal, so the IF filter cannot remove it. It is rejected before the mixer by a selective preselector/RF stage (α = √(1 + Q²ρ²) per tuned circuit), by choosing a higher IF so the image lies further away, by double conversion with a high first IF, or by an image-reject (quadrature) mixer.

  6. 6.Explain the concept of selectivity in the context of superheterodyne receivers.Concept

    Selectivity in superheterodyne receivers refers to the ability to distinguish between the desired signal and other signals at nearby frequencies. It is primarily determined by the quality of the IF filters, which are designed to allow only the desired frequency range to pass through while rejecting others.

  7. 7.Why are superheterodyne receivers often preferred over direct-conversion receivers?Application

    A direct-conversion (zero-IF) receiver mixes straight to baseband, so it suffers from DC offsets caused by LO self-mixing, 1/f noise, LO leakage out of the antenna and I/Q gain/phase mismatch. The superheterodyne does most of its gain and channel filtering at a fixed IF away from DC, avoiding these problems and allowing high-quality fixed crystal, ceramic or SAW filters. Its costs are the image problem and extra components; direct conversion wins on integration and is common in modern ICs.

  8. 8.A superheterodyne receiver has a local oscillator at 100 MHz and an IF of 10 MHz with high-side injection. Find the signal and image frequencies.Numerical

    With high-side injection the LO is above the signal, so f_s = f_LO − f_IF = 100 − 10 = 90 MHz. The image lies on the other side of the LO, also 10 MHz away: f_si = f_LO + f_IF = 110 MHz, which equals f_s + 2f_IF = 90 + 20 = 110 MHz. Both 90 MHz and 110 MHz produce a 10 MHz difference with the LO, which is why the 110 MHz image must be filtered before the mixer.

  9. 9.A superheterodyne receiver has an RF input frequency of 150 MHz and an IF of 10 MHz. What should be the local oscillator frequency?Numerical

    The local oscillator frequency (f_LO) can be either above or below the RF frequency. For a high-side injection, f_LO = f_RF + IF = 150 MHz + 10 MHz = 160 MHz. For a low-side injection, f_LO = f_RF - IF = 150 MHz - 10 MHz = 140 MHz.

  10. 10.What is the purpose of the mixer in a superheterodyne receiver?Concept

    The mixer in a superheterodyne receiver combines the incoming radio frequency (RF) signal with the local oscillator signal to produce the intermediate frequency (IF). This process, known as frequency mixing, is essential for converting the RF signal to a fixed IF, which can be more easily processed by the receiver's filters and amplifiers.

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