Communication Circuits

Tip

Exam Focus

High-yield items: low-level vs high-level AM (where the envelope is formed and the resulting PA class); balanced and ring modulators for DSB-SC and why symmetry suppresses the carrier; the envelope detector with $1/f_c\ll R_LC\ll 1/f_{m}$ and diagonal clipping; coherent/product detection with the $\cos\phi$ loss and beat from $\Delta\omega$; the FM discriminator S-curve and the slope/Foster–Seeley/ratio/PLL family (with differing limiter needs); and ASK/FSK/BPSK/QPSK generation and coherent vs noncoherent detection.

Communication theory defines a waveform; a communication circuit must create or recover it with real devices, biasing, filtering and synchronisation. Answers should label input, output, carrier/LO, filters and feedback paths, then state which unwanted terms are rejected.

Circuit Selection Map

Standard families of AM/DSB generation circuits: nonlinear (square-law), switching, four-quadrant multiplier/balanced and high-level collector/drain modulation.

Required waveform	Common generator	Common detector
Standard AM	Low-level multiplier or high-level collector/drain	Diode envelope detector
DSB-SC	Balanced/product or ring modulator	Coherent product detector
SSB-SC	DSB-SC $+$ filter, or phase-shift network	Product detector $+$ BFO/carrier recovery
FM	VCO/reactance modulator or Armstrong method	Discriminator, ratio detector or PLL
PM	Phase modulator	Phase detector/PLL, or discriminator $+$ integrator
ASK/OOK	Carrier switch/product modulator	Envelope or coherent detector
BFSK	VCO or two oscillators	Filter-energy detector, discriminator or correlator
BPSK/QPSK/QAM	Balanced I/Q product modulators	Coherent I/Q correlator receiver

Waveform-to-circuit selection map for generators and detectors.

Map of AM, DSB-SC, SSB, FM and direct-PM generation methods. PM may use a varactor phase shifter, vector/IQ modulator or PLL phase path; the exact device implementation varies.

Standard AM Modulators

The required standard-AM output and the no-overmodulation limit are

Caution

Key Formula — Standard AM waveform

$$v_o(t)=A_c\,[\,1+k_a m(t)\,]\cos\omega_c t,\qquad \left\lvert k_a m(t)\right\rvert\le 1 .$$

(a) Low-level AM modulates before RF amplification, so every following stage must be linear. (b) High-level AM lets an efficient Class-C final stage run while the audio amplifier varies its collector/drain supply.

Low-Level Modulator

Message and carrier combine at low power; the AM waveform is then amplified to transmitter output power. Methods: diode/transistor square-law modulator, four-quadrant analog multiplier, or a message-controlled variable-gain amplifier. Key requirement: every RF stage after modulation must preserve the envelope, so linear Class A/AB/B amplification is used, which lowers efficiency at high power.

High-Level Modulator

The unmodulated carrier is first amplified by an efficient nonlinear stage (commonly Class C) and the audio varies its collector/drain supply. For ideal $100\%$ sinusoidal collector/plate modulation the audio stage must supply about half the carrier power. Advantages: high RF efficiency, suits high transmitter power. Limitations: needs a high-power audio amplifier and a modulation transformer or supply modulator.

Feature	Low-level AM	High-level AM
Modulation point	Before RF power amp	At final RF power stage
Message power	Small	High
Following RF stages	Must be linear	Final may be Class C
Overall efficiency	Lower	Higher
Main use	Low/medium power, integrated	High-power broadcast

Low-level versus high-level AM generation.

DSB-SC Modulators

A product (balanced) modulator multiplies message and carrier so that the standalone carrier term cancels, leaving only the two sidebands (DSB-SC).

Caution

Key Formula — Product modulator output

$$v_o(t)=K\,m(t)\,A_c\cos\omega_c t .$$

For $m(t)=A_m\cos\omega_m t$,

$$v_o(t)=\frac{KA_cA_m}{2}\big[\cos(\omega_c+\omega_m)t+\cos(\omega_c-\omega_m)t\big],$$

with no carrier line at $\omega_c$.

Balanced product modulator: matched branches cancel carrier feedthrough while the cross-products add; a bandpass filter selects the DSB-SC band. Matched-diode, differential/Gilbert and push-pull realizations are common; device mismatch, transformer imbalance and offsets leave finite carrier suppression, quoted in dB against a stated sideband or carrier reference.

Practical balanced implementations use matched diodes, a differential pair or Gilbert-cell multiplier, or two amplitude modulators in push-pull. Their carrier-only terms cancel while the cross-products add. Device mismatch, transformer imbalance and DC offsets leave residual carrier, so carrier suppression in dB must state its reference: normally the wanted sideband level or the corresponding unsuppressed-carrier level.

Diode-Ring (Double-Balanced) Modulator

A strong carrier alternately forward-biases opposite diode pairs, reversing the message polarity at the carrier rate (multiplication by a square wave). By symmetry both carrier feedthrough and baseband feedthrough cancel; a bandpass filter selects $f_c\pm f_m$ and rejects the odd switching products $3f_c\pm f_m,\,5f_c\pm f_m,\dots$ A passive ring needs no DC bias, handles a wide dynamic range and is the classic double-balanced mixer.

Diode-ring (lattice) modulator: two center-tapped transformers, four diodes and the carrier across the centre taps. Both carrier and message feedthrough cancel, giving DSB-SC after filtering.

SSB Generation Circuits

SSB generation. (a) Filter method: DSB-SC then a sharp crystal/mechanical filter selects one sideband. (b) Phasing method: quadrature message and carrier in two product modulators; adding/subtracting cancels one sideband.

Filter method: a balanced modulator makes DSB-SC, a sharp bandpass filter passes only USB or LSB, and linear stages amplify it. For low message frequencies the sidebands crowd near $f_c$, demanding a highly selective crystal/mechanical filter or generation at a convenient IF followed by mixing.

Phasing method: using $90^\circ$-shifted message and carrier,

Caution

Key Formula — Phasing (Hartley) SSB

$$s_{\mathrm{USB}}(t)=m(t)\cos\omega_c t-\hat m(t)\sin\omega_c t,\qquad s_{\mathrm{LSB}}(t)=m(t)\cos\omega_c t+\hat m(t)\sin\omega_c t,$$

where $\hat m(t)$ is the Hilbert/$90^\circ$ version of $m(t)$.

The challenge is holding an accurate $90^\circ$ shift and equal amplitude over the whole band. The Weaver method uses two quadrature-mixing stages with low-pass filtering, avoiding a wideband audio Hilbert network and is common in DSP/SDR.

AM Demodulator Circuits

Envelope Detector

Diode envelope detector: $D$ charges $C$ near positive carrier peaks; between peaks $C$ discharges through $R_L$ following the envelope.

Between peaks $v_C(t)=V_0\,\mathrm{e}^{-t/(R_LC)}$. The time constant must exceed a carrier period yet track the fastest envelope:

Caution

Key Formula — Envelope-detector RC condition

$$\frac{1}{f_c}\ll R_LC\ll\frac{1}{f_{m(\max)}} .$$

For a single-tone AM envelope the sharper no-diagonal-clipping bound is

$$R_LC\le\frac{\sqrt{1-\mu^2}}{\mu\,\omega_m}.$$

Envelope detection. (a) Too-small $R_LC$ leaves carrier ripple. (b) Too-large $R_LC$ (orange) cannot follow the falling envelope (green dashed), cutting diagonally across it.

Distortion	Cause	Remedy
Carrier ripple	$RC$ too small	Increase $RC$ (still track envelope)
Diagonal clipping	$RC$ too large; $C$ cannot follow falling envelope	Reduce $RC$
Negative-peak clipping	AC load $<$ DC load (next stage shunts $R_L$)	Buffer / raise input impedance
Overmodulation	$\mu>1$, envelope crosses zero	Reduce modulation depth
Threshold distortion	Weak RF near diode drop	Biased/active or synchronous detector

Envelope-detector distortion mechanisms and remedies.

An envelope detector works only for transmitted-carrier AM with a faithful envelope; it cannot recover DSB-SC or SSB. A square-law detector uses $i=a_1v+a_2v^2$; the squared term yields a baseband component (good for small signals, distorts as level grows), and a low-pass filter rejects the RF and harmonic products while retaining that baseband term.

Product (Synchronous) Detector

Coherent product detector: multiply by a synchronised local carrier and low-pass filter. Used for DSB-SC and SSB.

Caution

Key Formula — Coherent detection with carrier error

For DSB-SC $s(t)=A_c m(t)\cos\omega_c t$ and LO $2\cos[(\omega_c+\Delta\omega)t+\phi]$,

$$v_o(t)=A_c m(t)\cos(\Delta\omega\,t+\phi)\ \xrightarrow{\ \Delta\omega=0\ }\ A_c m(t)\cos\phi .$$

Phase error scales the output by $\cos\phi$ (zero at $90^\circ$, inverted at $180^\circ$); a frequency error produces audible beat/fading. For SSB a BFO/ reinserted carrier is used and a frequency error shifts every recovered audio tone by $\Delta f$. Carrier recovery uses a Costas loop, squaring loop or transmitted pilot.

FM Generation Circuits

FM generation. (a) Direct: message varies an LC/VCO frequency, large deviation but poorer stability. (b) Indirect (Armstrong): integrate then phase-modulate a crystal carrier; multipliers scale carrier and deviation, whereas the mixer translates carrier without changing deviation.

Caution

Key Formula — Instantaneous frequency and PM

$$f_i(t)=f_c+k_f m(t),\qquad s_{\mathrm{PM}}(t)=A_c\cos\!\big[\omega_c t+k_p m(t)\big].$$

Direct FM (varactor, VCO, reactance modulator) gives large deviation; a PLL can stabilise the long-term centre frequency. FM is made from PM by integrating $m(t)$ first; PM from FM by differentiating first.

Armstrong Indirect FM

A crystal oscillator supplies a stable carrier; the message is integrated and applied to a phase modulator to produce narrowband FM. Frequency multipliers then scale both carrier frequency and deviation by their multiplication factor, whereas a mixer translates the carrier to another band without changing the deviation. Armstrong generation therefore gives excellent stability but needs extra stages and careful multiplier/mixer frequency planning.

Direct PM

Direct phase modulation may use a message-controlled varactor phase shifter, a vector/IQ modulator that rotates the carrier vector, or a PLL phase-control path. In every case the message controls instantaneous phase rather than directly setting the oscillator frequency.

FM Demodulator Circuits

Every FM detector converts frequency deviation to voltage with an ideally linear S-shaped characteristic through $f_c$:

Caution

Key Formula — Discriminator characteristic

$$v_o(t)\approx K_D\,[\,f_i(t)-f_c\,],$$

with $K_D$ in volts per hertz; output is zero at $f_c$ and opposite in sign above/below it.

Discriminator S-curve: linear through the centre frequency, saturating away from it.

The detector taxonomy places this slope method alongside balanced, ratio, PLL, and quadrature alternatives.

Taxonomy of FM detectors. A balanced slope detector subtracts oppositely detuned responses, extending symmetry and cancelling part of their common amplitude variation.

Slope Detector

Place $f_c$ on the linear slope of a detuned resonant circuit: a frequency change becomes an amplitude change, then an envelope detector recovers the message.

Slope detection: the tuned circuit is used off resonance so its skirt converts frequency deviation into amplitude. It has a narrow linear range and needs a preceding limiter.

A balanced slope detector subtracts two oppositely detuned responses for a wider, more symmetric range. Subtraction also cancels part of the common amplitude variation, but the detector remains AM-sensitive and still needs limiting.

Foster–Seeley and Ratio Detectors

Simplified Foster–Seeley discriminator: a center-tapped double-tuned transformer turns frequency deviation into a phase difference; the two rectified diode voltages are equal at $f_c$ and unequal off centre, and their difference is the audio. A ratio detector uses the same transformer with reversed diode/loading and a large capacitor holding the voltage sum constant, giving inherent AM rejection.

The Foster–Seeley circuit gives high output and very good linearity but responds to amplitude, so a preceding limiter is essential. The ratio detector trades a little linearity for built-in AM rejection and usually needs no separate limiter.

PLL FM Detector

PLL FM demodulator: the VCO tracks the input frequency; within lock the loop-filter control voltage is the recovered message. Its phase comparison is normally amplitude-insensitive, so no separate limiter is normally required.

Caution

Key Formula — PLL demodulator output

$$v_c(t)\approx\frac{f_i(t)-f_0}{K_{\mathrm{VCO}}} .$$

The PLL gives excellent linearity, amplitude immunity and easy IC integration; the loop bandwidth must follow the highest message frequency and deviation while rejecting noise. Because phase comparison is normally amplitude-insensitive, a PLL FM detector normally needs no separate limiter, although practical input conditioning may still limit or square a weak/noisy signal. A quadrature detector splits the limited FM into direct and frequency-dependent phase-shift paths and multiplies them—also IC-friendly.

Detector	Principle	Limiter?	Linearity	Feature
Slope	Detuned amplitude response	Yes	Poor	Simplest
Balanced slope	Difference of two slopes	Yes	Moderate	Symmetric
Foster–Seeley	Transformer phase imbalance	Yes	Very good	High output
Ratio	Ratio of diode voltages	Usually no	Good	AM rejection
PLL	VCO tracks $\Delta f$	Normally no	Excellent	IC-friendly
Quadrature	Frequency-dependent phase	Limited input	Good	IC-friendly

Comparison of FM detectors.

Digital Modulator and Demodulator Circuits

ASK/OOK: a unipolar bit drives an RF switch/multiplier, $s(t)=A_c b(t)\cos\omega_c t$; noncoherent detection uses BPF $\to$ envelope detector $\to$ LPF or matched filter $\to$ a clocked threshold, while coherent detection uses a recovered carrier and correlator. BFSK: bits drive a VCO/DDS or switch between two phase-continuous tones; noncoherent detection uses two bandpass/energy detectors, or a discriminator/PLL converts frequency to voltage. A coherent receiver uses two synchronized correlators and decides for the tone with the larger metric. BPSK: map bits to $\pm1$ into a balanced product modulator; a coherent receiver uses carrier recovery (Costas) $\to$ product detector $\to$ matched filter $\to$ zero threshold, with differential encoding resolving the $180^\circ$ ambiguity.

(a) BPSK: antipodal mapping into a balanced modulator. (b) QPSK: a serial-to-parallel mapper drives quadrature product modulators whose sum is the QPSK signal.

Caution

Key Formula — QPSK signal

$$s(t)=A\,[\,I(t)\cos\omega_c t-Q(t)\sin\omega_c t\,],\qquad I,Q\in\{\pm1\}.$$

For QPSK and QAM, mapped I and Q symbol streams are pulse-shaped before the two product modulators to control occupied bandwidth and intersymbol interference. After coherent I/Q down-conversion, matched filtering and timing recovery, QPSK uses quadrant/sign decisions while QAM selects the nearest allowed constellation point.

Generic coherent I/Q modem: pulse-shaped branches are quadrature modulated; matched filters and symbol timing feed a clocked decision. QPSK uses quadrant signs, while QAM chooses the nearest allowed constellation point.

QAM adds amplitude levels and needs a linear PA; constant-envelope FSK/MSK tolerates saturated PAs. Essential support blocks are carrier recovery (correct RF phase/frequency for coherent PSK/QAM), symbol-timing recovery (sample each matched-filter output at its optimum instant), frame sync (find word or packet boundaries), AGC (scale I/Q samples into the decision range), and equalisation (compensate channel amplitude/phase distortion and intersymbol interference).

Metric	Why it matters
Carrier / sideband suppression	Wasted power; image and coherent-scheme interference
EVM / modulation error	RMS constellation error vs ideal symbols
Frequency error / phase noise	Rotation, beat and degraded high-order QAM
Linearity (IP3) / PAPR	Intermodulation, spectral regrowth, PA back-off
Conversion gain and port isolation	Mixer/modulator level budget; blocks LO/RF/message leakage

Practical communication-circuit metrics.

Solved Examples

Note

Example — Low-level vs high-level AM generation (5 marks)

Standard AM needs $v_o(t)=A_c[1+k_a m(t)]\cos\omega_c t$ with $\left\lvert k_a m(t)\right\rvert\le1$. In low-level modulation, message and carrier combine at small power (square-law, multiplier or VGA); all following RF stages must be linear (Class A/AB/B), so efficiency is limited but the audio drive is tiny. In high-level modulation, a Class-C final stage is supply-modulated by a high-power audio amplifier, giving high RF efficiency at the cost of a modulation transformer and large audio power. For a $1\,kW$ carrier at $\mu=1$, total RF power is $1.5\,kW$ and the sidebands carry $0.5\,kW$, matching the $\approx P_c/2$ audio requirement.

Practice: draw both paths and make the PA-linearity vs audio-power trade-off explicit (about 7–8 min).

[!NOTE]

Example — Balanced and ring modulators (10 marks)

Both produce DSB-SC via $v_o(t)=Km(t)A_c\cos\omega_c t$; for a tone, $v_o=\tfrac{KA_cA_m}{2}[\cos(\omega_c+\omega_m)t+\cos(\omega_c-\omega_m)t]$ with no carrier line. In a balanced modulator matched branches receive the carrier in opposite symmetry, so carrier-only terms cancel while cross-products add; a BPF passes the DSB band. In a ring modulator a strong carrier switches opposite diode pairs, reversing message polarity each half cycle (multiplication by a square wave); double balance cancels both carrier and baseband feedthrough, and filtering removes $3f_c\pm f_m,\dots$ For a $5\,kHz$ tone on a $1\,MHz$ carrier the wanted lines are $995$ and $1005\,kHz$; absence of the $1000\,kHz$ line indicates good suppression. Mismatch and offsets set a finite suppression (dB); the same ring is the classic double-balanced mixer.

Practice: derive the sidebands, explain branch cancellation and alternate diode conduction, then list nonidealities (about 16–18 min).

[!NOTE]

Example — Envelope detector and RC design (10 marks)

A diode charges $C$ near positive peaks; between peaks $v_C=V_0\mathrm{e}^{-t/(R_LC)}$. Choose $1/f_c\ll R_LC\ll 1/f_{m(\max)}$; a too-small $RC$ leaves ripple, a too-large $RC$ causes diagonal clipping, and an AC load below the DC load gives negative-peak clipping (cured by a buffer); $\mu>1$ gives unavoidable overmodulation distortion. For $f_c=1\,MHz$, $f_m=5\,kHz$, $\mu=0.8$:

$$R_LC\le\frac{\sqrt{1-0.8^2}}{0.8(2\pi)(5000)}=\frac{0.6}{2.513\times10^{4}} \approx23.9\,\mu\mathrm{s},$$

while the carrier-period bound used above is $1/f_c=1\,\mu\mathrm{s}$, so $R_LC$ around $5\,$–$10\,\mu\mathrm{s}$ is safe; $R_L=10\,k\Omega$, $C=1\,nF$ gives $10\,\mu\mathrm{s}$.

Practice: draw charge/discharge paths, derive both bounds and name the four distortions (about 16–18 min).

[!NOTE]

Example — Product detection and carrier errors (10 marks)

A product detector multiplies the suppressed-carrier input by a recovered carrier and low-pass filters it, preserving signed $m(t)$. For DSB-SC with LO $2\cos[(\omega_c+\Delta\omega)t+\phi]$ the baseband output is $A_c m(t)\cos(\Delta\omega t+\phi)$; with $\Delta\omega=0$ it is $A_c m(t)\cos\phi$ (max at $0^\circ$, zero at $90^\circ$, inverted at $180^\circ$; $0.866$ at $30^\circ$). A frequency error causes fading/beat. For SSB a BFO error shifts every audio tone by $\Delta f$: a $20\,Hz$ error moves a $1\,kHz$ tone to $\approx 980$ or $1020\,Hz$. Carrier recovery uses a Costas/squaring loop or a pilot.

Practice: derive the LPF output in $\phi$ and $\Delta\omega$, then separate DSB fading from SSB frequency shift (about 16–18 min).

[!NOTE]

Example — Slope, Foster–Seeley, ratio and PLL FM detectors (10 marks)

All realise $v_o\approx K_D[f_i-f_c]$ with a linear S-curve. A slope detector uses a detuned tank skirt (narrow, AM-sensitive, needs a limiter). A Foster–Seeley discriminator converts deviation to a phase difference in a center-tapped transformer—high output and linearity but amplitude-sensitive, so a limiter is essential. A ratio detector holds the diode-voltage sum constant, giving inherent AM rejection with no separate limiter. A PLL forces the VCO to track $f_i$, so $v_c\approx(f_i-f_0)/K_{\mathrm{VCO}}$ is the message—excellent linearity and IC-friendly. For $K_{\mathrm{VCO}}=50\,kHz/V$ and $\Delta f=25\,kHz$ the peak output is $0.5\,V$. The limiter removes parasitic AM before amplitude-dependent detectors.

Practice: sketch the S-curve, explain each mechanism and tabulate limiter need vs linearity (about 16–18 min).

[!NOTE]

Example — ASK, BFSK, BPSK and QPSK circuits (10 marks)

ASK/OOK: a bit switches the carrier; noncoherent BPF $\to$ envelope detector $\to$ matched filter/LPF $\to$ clocked threshold, or coherent correlation—simple but amplitude-noise sensitive. BFSK: a VCO/DDS or phase-continuous tone switch selects two frequencies; two energy detectors (noncoherent), a discriminator/PLL, or two coherent correlators with a larger-metric decision recover the bit; it tolerates nonlinear PAs but uses more bandwidth. BPSK: $\pm1$ into a balanced modulator; coherent recovery $\to$ product detector $\to$ matched filter $\to$ zero threshold (differential coding fixes the $180^\circ$ ambiguity). QPSK: $s(t)=A[I\cos\omega_c t-Q\sin\omega_c t]$ carries two bits/symbol; pulse-shaped I/Q branches limit bandwidth, and the receiver down-converts, matched-filters and makes two sign decisions (Gray mapping limits neighbour errors to one bit). QAM uses the same chain with multilevel I/Q and a nearest-constellation-point decision. At $R_s=1\,MBd$, BPSK gives $1\,Mbit/s$ and QPSK $2\,Mbit/s$.

Practice: draw each modulator/detector, distinguish coherent from noncoherent and state all sync needs (about 17–19 min).

[!NOTE]

Key Point — Revision — Communication Circuits

• Low-level AM needs linear RF amplification after modulation; high-level AM modulates the efficient Class-C final stage.

• Balanced and ring modulators use symmetry to suppress the carrier and give DSB-SC; the ring also cancels baseband feedthrough.

• SSB $=$ one DSB-SC sideband filtered out, or quadrature phase cancellation (phasing/Weaver).

• Envelope detector: $1/f_c\ll R_LC\ll 1/f_m$; large $RC$ $\to$ diagonal clipping. DSB-SC/SSB need a product detector with $v_o\propto\cos\phi$.

• Direct FM varies an oscillator; Armstrong FM uses a stable phase modulator plus multipliers/mixers.

• FM detectors: slope and Foster–Seeley need a limiter; the ratio detector rejects AM; the PLL output is its control voltage.

• ASK/BFSK allow noncoherent detection; BPSK/QPSK/QAM normally use coherent I/Q correlators with carrier and timing recovery.