Analog Receivers

Tip

Exam Focus

High-yield items: the superheterodyne block diagram and the function of each stage; the mixer relation $f_{IF}=\left\lvert f_{LO}-f_s\right\rvert$ with high/low-side injection ($f_{LO}=f_s\pm f_{IF}$); the image frequency $f_{image}=f_s+2f_{IF}$ and why only RF preselection can reject it; TRF advantages/limitations; sensitivity vs. selectivity vs. fidelity; and the FM extras (limiter, discriminator, de-emphasis, AFC). Numericals on $f_{LO}$ and $f_{image}$ are near-certain.

Receiver Purpose and Classification

A radio receiver selects a desired modulated signal from the many signals at its antenna, amplifies it, demodulates it and reproduces the original information with acceptable strength and fidelity.

Its essential tasks are selection of the wanted carrier, low-noise amplification of a weak signal, frequency conversion to a fixed IF, demodulation to recover baseband, audio/data amplification, and automatic control of gain or tuning.

Receiver	Principle	Main merit	Main limitation
Crystal	Tuned circuit + diode, no gain	Simplest, no supply	Very low sensitivity/selectivity
TRF	Amplifies selected signal at RF	Simple signal path	Tracking, nonuniform bandwidth
Superheterodyne	Converts every RF to one fixed IF	High uniform gain/selectivity	Mixer, LO, image response
Direct-conversion	Mixes RF to zero IF (baseband)	Highly integrable	DC offset, $1/f$ noise, LO leakage

Main receiver types; for AM/FM broadcast the superheterodyne is standard.

Tuned Radio-Frequency (TRF) Receiver

In a TRF receiver the selected station is amplified at its original radio frequency; there is no mixer, local oscillator or IF stage.

TRF receiver: antenna $\to$ cascaded tuned RF amplifiers $\to$ envelope detector $\to$ AF amplifier $\to$ speaker; all resonators track together.

Working

The antenna receives many stations; each RF stage has a parallel resonant circuit tuned to the wanted carrier, all varied together by a ganged capacitor. Cascaded stages give gain and out-of-band rejection, an envelope detector recovers the AM message, and the AF amplifier drives the speaker.

Caution

Key Formula — Tuned-circuit resonance and bandwidth

$$f_0=\frac{1}{2\pi\sqrt{LC}},\qquad B=\frac{f_0}{Q}.$$

Because $Q$ is roughly constant, the absolute bandwidth $B$ grows with tuning frequency — so selectivity is not uniform across the band.

Advantages and Limitations

Note

Key Point — TRF trade-offs

• Advantages: simple, no frequency converter, no internal image response, good sensitivity/selectivity over a narrow range, low part count.

• Limitations: several tuned circuits must track accurately; bandwidth/selectivity vary with frequency; high RF gain $\to$ instability; hard to get high gain and narrow bandwidth at high RF; unsuitable for wide-range broadcast.

Superheterodyne Receiver

A superheterodyne receiver translates every selected RF carrier to a fixed intermediate frequency (IF), where most gain and channel selectivity are obtained.

Superheterodyne receiver: antenna $\to$ RF amp $\to$ mixer (fed by the local oscillator) $\to$ fixed-IF amp $\to$ detector $\to$ AF amp $\to$ speaker, with AGC feedback to the RF/IF stages.

Block	Function
Antenna / input network	Capture RF energy; provide initial band selection and impedance matching
RF amp / preselector	Select band, improve sensitivity, reject the image before mixing
Local oscillator (LO)	Tunable sinusoid tracking receiver tuning
Mixer	Multiply RF and LO to give sum and difference frequencies
IF filter/amplifier	Most gain and adjacent-channel selectivity at one fixed frequency
Detector	Recover the AM or FM message
AGC	Vary RF/IF gain so output stays usable over a wide input range
AF amplifier	Voltage and power gain for the loudspeaker

Superheterodyne block functions.

Frequency Conversion

The mixer produces $f_{LO}+f_s$ and $\left\lvert f_{LO}-f_s\right\rvert$; the IF filter keeps the difference.

Caution

Key Formula — Mixing and local-oscillator injection

$$f_{IF}=\left\lvert f_{LO}-f_s\right\rvert,\qquad f_{LO}=f_s+f_{IF}\ \text{(high-side)},\qquad f_{LO}=f_s-f_{IF}\ \text{(low-side)}.$$

Mixer frequency conversion: $f_{RF}$ and $f_{LO}$ in; the IF filter selects the difference $f_{IF}=\left\lvert f_{RF}-f_{LO}\right\rvert$ and discards the sum.

Common broadcast IFs are $455\,kHz$ (AM) and $10.7\,MHz$ (FM). A fixed IF gives steep repeatable filters, stable high gain, and one detector frequency; only the RF preselector and LO must track.

Image Frequency

An image frequency is an undesired RF that produces the same IF as the wanted signal for a given LO. After mixing the IF filter cannot separate it, so it must be rejected by the RF preselector.

Caution

Key Formula — Image frequency

$$f_{image}=f_{LO}+f_{IF}=f_s+2f_{IF}\ \text{(high-side)},\qquad f_{image}=f_s-2f_{IF}\ \text{(low-side)}.$$

Image response is reduced by a tuned RF preselector, a higher first IF (image sits farther away), multiple tuned RF circuits, or a dual-conversion plan (high first IF for image rejection, low second IF for sharp selectivity). Hence the design trade-off: high IF $\Rightarrow$ better image rejection, but low IF $\Rightarrow$ easier narrow channel filtering.

Receiver Performance Terms

Term	Meaning	Measure / consequence
Sensitivity	Usable output from a weak input	Min. usable RF input for a specified SNR
Selectivity	Accept wanted channel, reject nearby	IF bandwidth, shape factor, ACR
Fidelity	Reproduce message without distortion	Flat message-band response, low distortion
Signal-to-noise ratio	Recovered signal vs. noise power	Higher SNR $=$ clearer reception
Image rejection	Suppress the image input	Set by RF preselection and IF plan
Stability	Stay tuned without drift/oscillation	Depends on LO, AGC, circuit design

Receiver performance terms.

Narrowing the IF filter improves adjacent-channel selectivity, but a filter narrower than the modulation bandwidth cuts wanted sidebands and lowers fidelity.

AM Receiver

A practical AM broadcast receiver uses the superheterodyne chain above. The RF amp selects the station, the mixer converts to $\approx455\,kHz$, the IF filter passes carrier plus both sidebands, a diode envelope detector recovers the message (and a DC control component), and the AF stages drive the speaker. For maximum audio $f_m$:

Caution

Key Formula — AM IF passband

$$B_{IF}\ge 2f_m.$$

Automatic Gain Control (AGC)

AGC derives a slowly varying DC from the detected signal and uses it to lower RF/IF gain on strong stations and raise it on weak ones, giving nearly constant output, overload prevention and wider dynamic range. Its time constant is slow relative to the audio, so it follows average carrier level rather than removing modulation. AM limitations: amplitude noise is detected with the envelope; ACR depends heavily on IF filtering; a simple envelope detector cannot demodulate DSB-SC/SSB; fading changes recovered amplitude unless AGC compensates.

FM Receiver

An FM receiver also uses superheterodyne conversion, but its post-IF stages differ because information is carried by instantaneous frequency.

Superheterodyne FM receiver: RF amp $\to$ mixer/LO $\to$ IF amp $\to$ limiter $\to$ discriminator $\to$ de-emphasis $\to$ AF amp $\to$ speaker; a slow discriminator error feeds AFC back to the LO.

Limiter, Discriminator and De-emphasis

The limiter clips amplitude changes from noise/fading while keeping zero crossings, since ideal FM has constant envelope; it is essential before amplitude-sensitive slope and Foster–Seeley detectors (ratio and PLL detectors are less AM-sensitive). The discriminator converts frequency deviation to voltage with a linear S-curve: $v_o=0$ at $f_c$, positive on one side, negative on the other, and $v_o\propto f-f_c$ in the linear range.

Because FM noise power rises toward the top of the audio band, the transmitter applies pre-emphasis and the receiver a complementary first-order RC de-emphasis:

Caution

Key Formula — De-emphasis time constant

$$\tau=RC\quad(50\,\mu\mathrm{s}\ \text{or}\ 75\,\mu\mathrm{s}).$$

Automatic Frequency Control (AFC)

AFC uses a slowly varying component of the discriminator output to correct LO drift: if the IF center moves, the discriminator’s DC error (whose polarity shows tuning direction) drives a varactor/controlled oscillator back to correct tuning. AGC controls gain; AFC controls frequency — do not confuse them. FM merits: amplitude-noise rejection after limiting, capture effect, high fidelity above threshold, constant-envelope RF. Limitations: wider bandwidth, more complex circuitry, rapid SNR collapse below threshold, and need for accurate alignment.

AM vs. FM Receiver Comparison

Feature	AM superhet	FM superhet
Common IF	$455\,kHz$	$10.7\,MHz$
Information parameter	Carrier amplitude	Instantaneous frequency
Before detector	IF amplifier	IF amplifier $+$ limiter
Detector	Envelope / synchronous	Discriminator, ratio, quadrature, PLL
Post-detector	Audio coupling/filter	De-emphasis network
Automatic control	AGC important	AFC common; limiting reduces AGC need
Noise immunity	Lower (amplitude noise detected)	Better above threshold
Bandwidth	Narrower	Wider
Complexity	Lower	Higher

AM versus FM superheterodyne receivers.

Solved Examples

Note

Example — Superheterodyne AM receiver, IF and image (10 marks)

A superheterodyne converts every station to one fixed IF where most gain and selectivity are obtained; the mixer/IF give $f_{IF}=\left\lvert f_{LO}-f_s\right\rvert$. The RF preselector selects the band, improves sensitivity and rejects the image; the LO tracks tuning; the IF filter ( $\approx455\,kHz$ for AM ) supplies gain and adjacent-channel selectivity; an envelope detector recovers audio plus the AGC voltage; and the AF amplifier drives the speaker. AGC lowers gain for strong stations and raises it for weak ones with a slow time constant.

For high-side injection $f_{LO}=f_s+f_{IF}$ and the image is

$$f_{image}=f_{LO}+f_{IF}=f_s+2f_{IF}.$$

Once both reach the mixer they become the same IF, so RF preselection must reject the image; a higher IF separates it farther, a lower IF eases narrow filtering, and dual conversion gets both. The IF must pass carrier and both sidebands, so $B_{IF}\ge 2f_{m(\max)}$.

Practice target: 16–18 min; label every block and derive both IF and image relations.

[!NOTE]

Example — Tuned radio-frequency receiver (5 marks)

A TRF receiver selects and amplifies the station directly at RF — no mixer, LO or IF. Two or more RF stages use parallel resonant circuits tuned to the wanted carrier, ganged so all resonances track; a diode envelope detector recovers the AM message and the AF stages drive the speaker. For each tuned circuit $f_0=1/(2\pi\sqrt{LC})$ and $B=f_0/Q$.

Advantages: simple path, low part count, no internal image, useful over a narrow range. Limitations: hard multi-resonator tracking, changing absolute bandwidth when $Q\approx$ const, limited stable gain at high RF, nonuniform selectivity. With $Q=100$, $B\approx5.5\,kHz$ at $550\,kHz$ but $\approx16\,kHz$ at $1.6\,MHz$ — one end cuts sidebands, the other admits neighbours. The superheterodyne fixes this with a fixed IF.

Practice target: 7–8 min; draw the cascaded stages and use $B=f_0/Q$.

[!NOTE]

Example — Local-oscillator and image-frequency numerical (5 marks)

Given $f_s=1.000\,MHz$, $f_{IF}=455\,kHz$ and high-side injection:

$$f_{LO}=f_s+f_{IF}=1.000+0.455=1.455\,MHz,$$$$f_{image}=f_s+2f_{IF}=1.000+2(0.455)=1.910\,MHz.$$

Check: $\left\lvert 1.455-1.000\right\rvert=0.455\,MHz$ and $\left\lvert 1.910-1.455\right\rvert=0.455\,MHz$, so both inputs become $455\,kHz$ after mixing. The IF filter cannot separate them; the RF preselector must attenuate $1.910\,MHz$. Image separation is $2f_{IF}=910\,kHz$. Low-side injection would give $f_{LO}=f_s-f_{IF}$ and $f_{image}=f_s-2f_{IF}$.

Practice target: 7–8 min; write the injection relation first and verify both inputs give the same IF.

[!NOTE]

Example — Superheterodyne FM receiver (10 marks)

An FM superhet selects a station, converts to a fixed IF ( $\approx10.7\,MHz$ ) and recovers the message from frequency deviation. RF amp gives low-noise gain and image rejection; the mixer/LO satisfy $f_{IF}=\left\lvert f_{LO}-f_s\right\rvert$; the IF passes the full FM channel $\approx 2(\Delta f+f_{m(\max)})$ (Carson). The limiter removes AM noise while keeping zero crossings; the discriminator gives an S-curve $v_o\propto f-f_c$; de-emphasis ($\tau=RC=75\,\mu\mathrm{s}$ for $R=75\,k\Omega$, $C=1\,nF$) inverts pre-emphasis and cuts HF noise; AFC corrects LO drift from the discriminator DC error.

For $\Delta f=75\,kHz$, $f_{m(\max)}=15\,kHz$, Carson bandwidth $=2(75+15)=180\,kHz$, motivating an IF channel near $200\,kHz$. FM offers limiting, capture effect and high fidelity above threshold at the cost of bandwidth and complexity.

Practice target: 16–18 min; explain limiter, discriminator, de-emphasis and AFC as four distinct functions.

[!NOTE]

Example — Sensitivity, selectivity and fidelity (5 marks)

Sensitivity is the minimum RF input giving a specified output SNR/SINAD; it depends on first-stage noise figure, gain and detector threshold. Selectivity is acceptance of the wanted channel and rejection of neighbours, set by IF bandwidth, shape factor and image rejection. Fidelity is distortion-free reproduction, requiring the passband to include all modulation components; for AM audio $f_m$, $B_{IF}\gtrsim 2f_m$.

Trade-off: narrowing IF lowers admitted noise $N=kTB$ and interference (better sensitivity/selectivity), but below the wanted spectrum it cuts sidebands and hurts fidelity. For a $455\,kHz$ IF carrying $5\,kHz$ audio, $\approx10\,kHz$ passband is needed, i.e. $Q=f_0/B\approx 45.5$. Design balances minimum signal, rejection and message bandwidth.

Practice target: 7–8 min; define all three with a measurable criterion and one numerical.

[!NOTE]

Key Point — Revision — Analog Receivers

• TRF amplifies at incoming RF; superheterodyne converts to a fixed IF.

• Mixer: $f_{IF}=\left\lvert f_{LO}-f_s\right\rvert$; injection $f_{LO}=f_s\pm f_{IF}$.

• Image (high-side): $f_{image}=f_s+2f_{IF}$; only RF preselection rejects it.

• High IF $\Rightarrow$ better image rejection; low IF $\Rightarrow$ easier selectivity.

• Typical IF: $455\,kHz$ (AM), $10.7\,MHz$ (FM).

• AGC stabilises level; AFC corrects LO drift — not interchangeable.

• FM adds limiter, discriminator and de-emphasis ($\tau=RC$).

• Sensitivity $=$ weak signals; selectivity $=$ unwanted channels; fidelity $=$ message reproduction.