Superheterodyne Receiver

How a superheterodyne receiver works

The problem the superheterodyne solves is deceptively annoying. A radio station occupies a narrow slice of spectrum — an AM channel is about 10 kHz wide — but it can sit anywhere on the dial, from 540 kHz to 1600 kHz. To pull one station out cleanly you need a bandpass filter sharp enough to pass 10 kHz and reject its neighbor 9 kHz away. Building one fixed filter that sharp is routine. Building one that stays exactly 10 kHz wide while you slide its center frequency across the whole band, in lockstep with several other stages, is a nightmare. Tunable sharp filters drift, their bandwidth widens with frequency, and ganging three of them to track perfectly is mechanically brutal.

Edwin Armstrong's 1918 insight was to stop trying. Instead of moving the filter to the signal, move the signal to the filter. Take whatever station you want, multiply it by a locally generated sine wave, and the multiplication produces new frequencies — the sum and the difference of the two inputs. Pick the local oscillator so the difference always lands on one fixed frequency, the intermediate frequency (IF). Now every station, wherever it lives on the dial, arrives at the IF stage at exactly the same frequency. One fixed, sharp, high-gain filter-and-amplifier chain does the hard work for all of them. The only thing that tunes is the local oscillator.

The signal chain, in order:

• Antenna + RF preselector. A loosely tuned bandpass stage that picks the rough neighborhood of the desired station and — critically — rejects the image frequency (more below). Often a single tuned LC stage with modest selectivity plus an RF amplifier (the LNA) to set the noise figure.
• Local oscillator (LO). A tunable oscillator that runs at f_LO = f_RF + IF (usually high-side injection). On the dial of an old radio, this is the second section of the ganged tuning capacitor.
• Mixer. A deliberately nonlinear (or switching) device that multiplies RF by LO. Its output contains f_RF + f_LO and |f_RF − f_LO| = IF, plus the originals. Everything but the IF gets filtered away next.
• IF amplifier + IF filter. The heart of the radio. Several tuned stages (or one ceramic/crystal/SAW filter) fixed at the IF, providing the bulk of the selectivity and 60–100 dB of gain.
• Demodulator (detector). An envelope detector for AM, a quadrature/ratio detector or PLL for FM, recovering the audio or data.
• AGC + audio amplifier. Automatic gain control feeds back from the IF to flatten signal-strength swings; the audio stage drives the speaker.

The math of mixing

A mixer is a multiplier. Feed it two sinusoids and use the product-to-sum identity:

cos(2π f_RF t) · cos(2π f_LO t)
   = ½ cos(2π (f_LO − f_RF) t)   ← difference term (the IF)
   + ½ cos(2π (f_LO + f_RF) t)   ← sum term (filtered out)

Intermediate frequency:   f_IF = | f_LO − f_RF |
Local oscillator (high-side injection):   f_LO = f_RF + f_IF

The local oscillator must track the signal so that the difference is always the same constant IF. The catch — and the defining weakness of the architecture — is that the absolute value hides a second solution. Two different RF inputs produce the same IF:

Wanted:  f_RF                with  f_LO = f_RF + f_IF
Image:   f_image = f_RF + 2·f_IF     (for high-side LO)

Check:   | f_LO − f_image | = | (f_RF + f_IF) − (f_RF + 2 f_IF) | = f_IF  ✓

So an unwanted station sitting 2×IF above the one you want sails straight through the mixer onto the same IF. The RF preselector before the mixer is the only thing standing in its way. This is why the choice of IF is the central design trade-off: a higher IF pushes the image 2×IF farther from the signal (easier for the RF stage to reject), but a lower IF makes the fixed IF filter narrower and cheaper for adjacent-channel selectivity. You cannot optimize both at once with a single conversion — hence double conversion.

The required filter quality factor makes the case for fixing the frequency. To pass a bandwidth B at a center frequency f, you need:

Q = f_center / B

At a fixed AM IF:   Q = 455 kHz / 10 kHz  ≈ 45     (easy LC or ceramic)
Tuning at the band top:   Q = 1600 kHz / 10 kHz ≈ 160   (hard, and must track)

Worked example: tuning an AM station at 1000 kHz

Take a textbook AM broadcast receiver with the standard 455 kHz IF, high-side LO injection, and you want to listen to a station broadcasting at 1000 kHz.

Wanted station:   f_RF  = 1000 kHz
IF:               f_IF  = 455 kHz
Local oscillator: f_LO  = f_RF + f_IF = 1000 + 455 = 1455 kHz

Mixer difference: 1455 − 1000 = 455 kHz   → into the IF strip ✓
Mixer sum:        1455 + 1000 = 2455 kHz   → rejected by IF filter

Image frequency:  f_image = f_RF + 2·f_IF = 1000 + 910 = 1910 kHz
Check the image:  1910 − 1455 = 455 kHz    → also lands on the IF ✗

Now move the dial to a station at 1400 kHz. The LO must move to 1855 kHz to keep the difference at 455 kHz. That single tracking requirement — LO always 455 kHz above the signal — is the only thing the ganged tuning capacitor's second section has to do. The IF filter never moves.

The image at 1910 kHz is 910 kHz away from the wanted 1000 kHz. A simple RF preselector tuned to 1000 kHz with a Q of only about 50 will already be tens of dB down at 1910 kHz, so a single-conversion AM radio rejects its image adequately. Push the same trick up to a 100 MHz FM signal with the same 455 kHz IF and the image would be only 910 kHz away — essentially impossible for an RF stage to reject — which is exactly why FM uses a much higher 10.7 MHz IF, putting its image a comfortable 21.4 MHz away.

The IF trade-off and double conversion

Every superhet design fights the same tension:

• High IF → good image rejection, poor selectivity. A high IF moves the image far away so the RF stage can kill it, but a high-frequency filter struggles to be narrow enough to separate adjacent channels (Q gets large).
• Low IF → good selectivity, poor image rejection. A low IF lets a cheap narrow filter give razor selectivity, but the image is close to the signal and the RF stage can't reject it.

Double conversion breaks the deadlock by using both. A high first IF (commonly 45 MHz, 70 MHz, or 10.7 MHz for HF gear) is chosen purely for image rejection: the first image is pushed far enough that the RF preselector handles it easily. Then a second mixer drops the signal to a low second IF (455 kHz or 10.7 MHz) where a narrow crystal, ceramic, or mechanical filter delivers the final adjacent-channel selectivity. The penalty is a second oscillator and the risk of internally generated spurs and birdies where the two LOs and their harmonics mix. Communications receivers, VHF/UHF scanners, and satellite tuners are almost all double or triple conversion.

Other recurring design knobs: high-side vs low-side LO injection (high-side is standard because it keeps the LO tuning range a smaller percentage span); the mixer type (diode ring, Gilbert-cell active mixer, or a passive FET switching mixer — each trades conversion gain, noise, and linearity); and where to put the gain (too much gain ahead of the mixer hurts the receiver's ability to handle strong nearby signals, quantified by the third-order intercept point, IP3).

Real-world IFs and architectures

System	Signal band	IF(s)	Conversions	Notes
AM broadcast radio	540–1600 kHz	455 kHz	Single	LC / ceramic IF filter, envelope detector
FM broadcast radio	88–108 MHz	10.7 MHz	Single	Ceramic or crystal IF, ~200 kHz wide
Shortwave / ham HF rig	1.8–30 MHz	45 MHz then 455 kHz	Double (up-conversion)	High 1st IF for image-free tuning
Analog TV (NTSC)	VHF/UHF channels	45.75 MHz video, 41.25 MHz sound	Single (to a common IF)	One tuner front-end for all channels
VHF/UHF scanner	30 MHz–1 GHz	e.g. 380 MHz → 10.7 MHz → 455 kHz	Triple	Tames wideband image and spur problems
GPS receiver	1575.42 MHz (L1)	~4–70 MHz then digital	Single/double then DSP	Final selectivity in the digital domain
Cell phone / Wi-Fi	0.7–6 GHz	Zero-IF (baseband) or low-IF	Direct conversion	I/Q mixing kills the image without a high IF

Superheterodyne vs other receiver architectures

	Superheterodyne	TRF (tuned RF)	Direct conversion (zero-IF)	Regenerative
Selectivity	Excellent (fixed IF)	Poor, widens with f	Good (set by baseband filters)	Fair, fiddly
Sensitivity	High (lots of IF gain)	Moderate	High	High but unstable
Image problem	Yes — needs preselector	None	None (I/Q cancels it)	None
Tunable elements	One (the LO)	Several ganged stages	One (the LO, at signal freq)	One
Main weakness	Image + LO leakage + spurs	Tracking, drift, bandwidth	DC offset, 1/f noise, I/Q imbalance	Re-radiation, unstable
Parts count / cost	Moderate	Low but bulky	Low (highly integrated)	Very low
Where it lives	Almost all radios since 1930s	Earliest 1920s sets, some sensors	Phones, SDR front-ends, ICs	Hobby kits, simple toys

Where it's used

• AM/FM broadcast radios. The canonical 455 kHz and 10.7 MHz IFs are a direct legacy of the superhet's dominance. Nearly every car radio, clock radio, and boombox built since the 1930s is a single-conversion superhet.
• Television tuners. Analog TV used a single down-conversion to a common 45.75/41.25 MHz IF so one front-end could receive any channel; the same idea persists in digital TV tuner chips.
• Cellular base stations and handsets. Classic 2G/3G phones used superheterodyne (often with a SAW IF filter); modern phones favor direct-conversion transceivers but still heterodyne — they just do the IF work at baseband in silicon.
• Radar and electronic warfare. Pulse radars down-convert the echo to an IF where matched filtering and Doppler processing happen; double conversion is standard for image and spur control across wide bands.
• Ham radio and shortwave. Communications receivers are the showcase of multi-conversion superhet design, with up-conversion to a high first IF and roofing filters that set the receiver's dynamic range.
• Software-defined radio. Most SDR front-ends are low-IF or zero-IF heterodyne receivers feeding an ADC; the filtering and demodulation that an old radio did with iron and crystals are now done with arithmetic.

Common misconceptions and pitfalls

• "The mixer adds the frequencies." A mixer multiplies; multiplication of two sinusoids produces both the sum and the difference. The superhet uses the difference. Calling it a "frequency adder" hides why the sum term and the image even exist.
• "Heterodyning shifts the signal, so nothing is lost." The conversion is lossy and noisy. A passive diode mixer has roughly 6–7 dB of conversion loss and a noticeable noise figure, which is exactly why a low-noise RF amplifier sits ahead of it to set the system noise figure before that loss.
• "A higher IF is always better." A higher IF helps image rejection but hurts adjacent-channel selectivity for a given filter technology. The right answer is usually two IFs, not one extreme.
• "The image is just noise." The image is a real, fully formed second station (or interferer) that lands on the IF as cleanly as the wanted signal. If a strong transmitter happens to sit at f_RF ± 2·IF, a poorly preselected receiver will demodulate it as if it were the station you tuned.
• "LO leakage doesn't matter." The local oscillator can leak back out the antenna and radiate. Early superhets were notorious local interferers; this is why the RF stage's reverse isolation and shielding matter, and why direct-conversion radios fight LO-to-RF self-mixing that creates DC offsets.
• "Tracking is automatic." In a single-knob analog superhet the RF preselector and the LO must both move together and stay exactly IF apart across the band. This is achieved with a padder/trimmer capacitor and a specially shaped LO tuning section — get it wrong and the radio is sensitive at one end of the dial and deaf at the other.