7. Receivers: TRF and the Triumph of the Superheterodyne

We have talked about modulation. Now: how do you actually pull a signal out of the air?

7.1 Tuned Radio Frequency (TRF) receiver

The natural first design: cascade an RF amplifier, a detector, and an audio amplifier, with a single tunable bandpass filter at the front to select the desired station.

Antenna ─► [Tunable RF amp/filter] ─► [Detector] ─► [Audio amp] ─► Speaker

Problems:

• The RF filter must be tunable across the entire receive band (say 540 to 1600 kHz for AM broadcast). Tuning a single high-Q filter across a 3:1 frequency range while maintaining narrow bandwidth is hard.
• Selectivity (how narrow the filter can be made) varies dramatically across the band because Q tends to scale with frequency.
• Gain at RF is hard. RF transistors are expensive and prone to oscillation; getting 100 dB of gain at MHz frequencies requires careful neutralization.

TRF receivers existed in the 1920s and were abandoned by 1930. They survive only as toys and educational kits.

7.2 The superheterodyne breakthrough

Edwin Armstrong (the same person who invented FM) patented the superheterodyne receiver in 1918, and it has been the dominant receiver architecture ever since.

The idea: instead of trying to achieve all the receiver's gain and selectivity at the RF, translate the RF down to a fixed intermediate frequency (IF) by mixing it with a tunable local oscillator. The IF strip (filter + amplifier) is then at a single frequency, and can be designed once for excellent gain and selectivity without ever needing to tune. Only the LO and a coarse RF preselector tune.

When the user turns the dial, only $f_\text{LO}$ changes. The IF stays at, say, 455 kHz for AM broadcast or 10.7 MHz for FM broadcast. The relationship is

$f_\text{IF} = |f_\text{RF} - f_\text{LO}|$

For a 1000 kHz desired RF and a 455 kHz IF: $f_\text{LO}$ is either 545 kHz (low-side injection) or 1455 kHz (high-side injection). Most AM receivers use high-side injection because the LO tunes a 2:1 range (995 to 2055 kHz) instead of needing to span across the IF.

7.3 Why this is genius

Three reasons:

1. All the gain is at one fixed frequency. A multi-stage IF amp can be designed once and reused across the entire receiver tuning range. Decades of optimization went into 455 kHz IF transformers and 10.7 MHz ceramic filters; you just buy them.
2. All the selectivity is at one fixed frequency. The IF filter sets the receiver bandwidth. Want a 6 kHz channel? Design a 6 kHz filter once. The RF preselector only needs to be wide and crude; it just rejects gross out-of-band signals and the image (next subsection).
3. The architecture extends naturally to multiple IFs. A "double-conversion" receiver mixes down to a high IF (say 70 MHz), then down again to a low IF (455 kHz), gaining the benefits of both wide-tunable RF (high IF places the image far away) and narrow selectivity (low IF allows high-Q filters).

7.4 The image problem

The mixer is a multiplier. When you multiply two sinusoids, you get the sum and the difference frequencies:

$\cos(2\pi f_\text{RF} t)\cdot\cos(2\pi f_\text{LO} t) = \tfrac{1}{2}\cos\!\big(2\pi(f_\text{RF} - f_\text{LO})t\big) + \tfrac{1}{2}\cos\!\big(2\pi(f_\text{RF} + f_\text{LO})t\big)$

The IF filter selects the difference. But two RF frequencies produce the same IF: $f_\text{RF} = f_\text{LO} + f_\text{IF}$ and $f_\text{RF} = f_\text{LO} - f_\text{IF}$. The unwanted one is the image frequency, and it is separated from the desired RF by exactly $2 f_\text{IF}$.

Example. AM receiver tuned to 1000 kHz with $f_\text{IF} = 455$ kHz, high-side LO at 1455 kHz. Image is at 1455 + 455 = 1910 kHz. A station at 1910 kHz would be received simultaneously on the same dial setting unless the RF preselector blocks it.

The RF preselector's job is image rejection. With $f_\text{IF} = 455$ kHz, the image is 910 kHz from the desired signal, an easy filtering job. If the IF were 50 kHz, the image would be only 100 kHz away from the desired signal, which is much harder to filter at MHz frequencies.

This drives the choice of IF:

• Low IF: easy to build narrow filters (high Q), but image is close to the signal and hard to reject.
• High IF: image is far away and easy to reject, but filter bandwidth-to-frequency ratio gets ugly (a 6 kHz channel at 10.7 MHz IF needs Q = 1800).

The compromise drives the canonical IFs: 455 kHz for AM (image rejection adequate, narrow filters easy with crystal lattices), 10.7 MHz for FM (image is far, ceramic filters give 200 kHz bandwidth). Modern radios often double-convert, mixing down to a high first IF (50 to 100 MHz), filtering for image rejection, then mixing down again to a low second IF (455 kHz or even lower) for narrow channel selectivity.

7.5 AGC: automatic gain control

Stations vary enormously in received signal strength: the local 50 kW transmitter at 1010 kHz might deliver volts to your antenna, while a distant 10 kW station at 1090 kHz delivers microvolts. Without compensation, you would deafen yourself when tuning to the strong one and hear nothing on the weak one.

AGC monitors the average level of the IF (or detector) output and adjusts the gain of one or more IF stages (and sometimes the RF stage) to keep the output level roughly constant. Implemented as a slow feedback loop (time constant of 50 ms to 1 s). Strong signal: gain reduced. Weak signal: gain at maximum.

Hardware-security tie-in: AGC and intentional jamming. An attacker who blasts a strong off-frequency tone into the receiver's RF range can saturate the AGC, forcing the receiver to crank its gain way down. The legitimate signal is now below the system noise floor, even though a frequency-selective filter would have rejected the jammer perfectly. This is the "front-end overload" attack, and it has been used to deny GPS reception to UAVs by transmitting strong off-frequency garbage that swamps the LNA before the IF filter can clean it. Counter-defenses include LNAs with high IP3, fast attack/slow decay AGC, and pre-LNA RF filters that reject out-of-band garbage.

7.6 AFC and squelch

AFC (Automatic Frequency Control) uses the discriminator's DC output to nudge the LO toward the correct center frequency. Drift of a free-running LO by 50 ppm at 100 MHz is 5 kHz, enough to detune a narrow channel. AFC closes the loop and holds the LO on station.

Squelch mutes the audio when no signal is received, suppressing the rush of noise that an FM receiver puts out below threshold. Implementation: detect the noise level (high-frequency noise above the audio band is a good proxy for the absence of a signal in the band) and mute when it exceeds a threshold. Older squelch was a simple comparator on the noise band; modern digital squelch uses CTCSS or DCS subaudible tones to enable only when a specific encoded tone is present, which is how dispatchers can have multiple users on the same frequency without each hearing the others.

7.7 Sensitivity, selectivity, fidelity

Three figures of merit:

Sensitivity is the smallest input signal that produces an acceptable output SNR. Limited by the noise figure of the receiver front end (Friis again: it is the LNA that matters most). Specified in microvolts (e.g., "1 µV for 12 dB SINAD") or in dBm.

Selectivity is the rejection of nearby channels. Set by the IF filter shape. A "good" channel filter is flat across the desired channel and falls off sharply (60 dB) within one channel width on either side. Modern crystal filters and DSP filtering achieve this routinely.

Fidelity is the faithfulness of the recovered audio. Set by the demodulator linearity, the audio chain bandwidth, and the absence of intermodulation distortion in the IF strip.

These three figures fight each other. Wider IF filters give better fidelity but worse selectivity. Higher IF gives better image rejection but worse selectivity per filter. The art of receiver design is balancing these.