Communication Circuits¶

Exam-ready answer

Standard AM requires

with \(|k_am(t)|\leq1\) for a nonreversing envelope. The two transmitter methods differ mainly in where this waveform is formed and therefore in power-amplifier class.

In low-level modulation, a diode/transistor square-law circuit, analog multiplier or variable-gain amplifier combines message and carrier at small power. Buffer, driver and final RF stages then raise the already modulated signal to antenna power. Every following RF stage must preserve amplitude, so Class A, AB or B linear amplification and suitable back-off are required. The message amplifier is low power and the circuit is easy to control, but linear RF efficiency is limited and nonlinearity causes envelope distortion/spectral regrowth.

In high-level modulation, the unmodulated carrier is first amplified by an efficient Class-C or switching RF final stage. A high-power audio amplifier varies its collector/drain supply or another final-stage parameter, creating AM at output power. This gives high RF efficiency and suits broadcast transmitters, but needs a modulation transformer or supply modulator and substantial audio power; for ideal \(100\%\) sinusoidal plate/collector modulation, peak audio power capability is approximately \(P_c/2\) under the classical assumptions.

Thus low-level AM uses little audio power but requires linear RF power gain after modulation; high-level AM permits an efficient nonlinear RF final stage but transfers the power burden to the audio modulator. For a \(1\,\text{kW}\) carrier at \(\mu=1\), total RF power is \(1.5\,\text{kW}\) and sidebands total \(0.5\,\text{kW}\), consistent with the approximate high-level audio requirement. Low-level is common in low/medium-power integrated transmitters; high-level is favored at high broadcast power.

Practice target: 7-8 minutes; draw both paths and make the PA-linearity versus audio-power trade-off explicit.

Exam-ready answer

A balanced or ring modulator generates DSB-SC by multiplying message and carrier while using symmetry to cancel direct feedthrough. For ideal multiplication,

If \(m(t)=A_m\cos\omega_mt\),

The output contains USB and LSB but no standalone \(\omega_c\) carrier term.

In a balanced modulator, matched diode/transistor branches receive the carrier with equal magnitude and opposite symmetry. Their carrier-only responses cancel at the output transformer/differential node, while the message-carrier cross-products have the polarity required to add. Implementations include push-pull modulators, differential pairs and Gilbert cells. A bandpass filter passes the DSB band and rejects harmonics. Device mismatch, bias offset and transformer imbalance cause residual carrier; carrier suppression is therefore a finite dB specification, not absolute in hardware.

In a diode-ring double-balanced modulator, a strong LO alternately forward-biases opposite diode pairs. The message transformer's output polarity is reversed every half carrier cycle, approximating multiplication by a bipolar square wave. The fundamental square-wave component translates the message to \(f_c\pm f_m\); odd LO harmonics also create \(3f_c\pm f_m\), \(5f_c\pm f_m\), etc., so output filtering is essential. Double balance ideally cancels both carrier/LO feedthrough and baseband/RF feedthrough and gives useful port isolation. A passive ring needs no DC bias, tolerates large signals and has good linearity, but has conversion loss and requires adequate LO drive plus baluns/transformers.

For a \(5\,\text{kHz}\) tone and \(1\,\text{MHz}\) carrier, the wanted output components are \(995\) and \(1005\,\text{kHz}\); absence of a \(1000\,\text{kHz}\) line indicates ideal suppression. Compared with a single-balanced circuit, the ring suppresses both input feedthrough families and many even-order terms, but balance errors and diode capacitance reduce isolation at high frequency. The same ring topology is used as a mixer because multiplication produces controlled sum/difference translation. DSB-SC saves carrier power but keeps \(2B_m\) bandwidth and requires coherent detection.

Practice target: 16-18 minutes; derive the sidebands, explain branch cancellation and alternate diode-pair conduction, then list practical nonidealities.

Exam-ready answer

An envelope detector recovers the message from standard transmitted-carrier AM using a diode followed by a parallel load resistor \(R_L\) and capacitor \(C\).

Near each positive carrier peak, the input exceeds capacitor voltage plus diode drop, the diode conducts and charges \(C\) rapidly to the new envelope. Between peaks the diode is reverse-biased and \(C\) discharges exponentially through \(R_L\):

The time constant must be long compared with a carrier period to suppress RF ripple but short compared with the fastest envelope variation:

as a cycle-based engineering rule. Using angular frequency, the corresponding lower scale is \(1/\omega_c\). For a sinusoidal AM envelope, the steepest falling slope gives the more restrictive approximate no-diagonal-clipping condition

If \(R_LC\) is too small, the capacitor discharges appreciably between carrier peaks, leaving carrier ripple at the output. If it is too large, the stored voltage cannot follow a rapidly falling envelope; the diode remains off and the exponential discharge cuts diagonally across the desired waveform, causing diagonal clipping. Negative-peak clipping occurs when the AC message load is lower than the DC detector load, often because the following amplifier/coupling network shunts \(R_L\); the negative envelope requires more discharge than the circuit permits. A high-input-impedance buffer or correctly designed coupling removes this unequal loading. For \(\mu>1\), the transmitted envelope itself crosses zero, so no RC choice can prevent overmodulation distortion. Diode threshold also distorts weak signals; biased/active or synchronous detectors improve low-level operation.

For \(f_c=1\,\text{MHz}\), \(f_m=5\,\text{kHz}\) and \(\mu=0.8\), the modulation-dependent upper bound is

The carrier angular-time scale is \(1/(2\pi f_c)=0.159\,\mu\text{s}\), so a value around \(5\)-\(10\,\mu\text{s}\) is plausible after accounting for diode/source/load details. For \(R_L=10\,\text{k}\Omega\), \(C=1\,\text{nF}\) gives \(10\,\mu\text{s}\). Envelope detection is simple and needs no local oscillator, but works only when a transmitted carrier creates a faithful envelope; ordinary DSB-SC and SSB require coherent detection.

Practice target: 16-18 minutes; draw charge/discharge current paths, derive both RC inequalities, and distinguish ripple, diagonal, negative-peak and overmodulation distortion.

Exam-ready answer

A product or synchronous detector multiplies a suppressed-carrier input by a locally reconstructed carrier and low-pass filters the result. It preserves the signed message and is therefore used for DSB-SC and SSB.

For DSB-SC

and local oscillator \(2\cos[(\omega_c+\Delta\omega)t+\phi]\), multiplication gives sum and difference terms. After the LPF removes the component near \(2\omega_c\),

With exact frequency, \(\Delta\omega=0\), the recovered output is \(A_cm(t)\cos\phi\). A phase error therefore attenuates and possibly inverts the output: \(\phi=0^\circ\) gives maximum, \(90^\circ\) gives zero, and \(180^\circ\) gives inverted message. At \(30^\circ\), amplitude is \(\cos30^\circ=0.866\) of ideal. Frequency error makes the multiplier vary with time and produces periodic fading/beating; even a small offset prevents stationary recovery.

For SSB, a BFO/PLL carrier translates the one RF sideband back to its original baseband. A carrier-frequency error does not merely cause a common fade: it shifts every recovered audio frequency by \(\Delta f\), changing speech pitch and intelligibility. Phase error rotates the recovered analytic signal and changes the mixture of message/Hilbert components. Accurate frequency is therefore especially important in narrowband SSB voice; a \(20\,\text{Hz}\) BFO error shifts a \(1\,\text{kHz}\) tone to approximately \(980\) or \(1020\,\text{Hz}\) depending on sideband/injection.

Carrier recovery methods are a transmitted pilot/residual carrier, squaring loop for suitable suppressed-carrier waveforms, Costas loop for DSB/PSK, or a manually/automatically controlled BFO for SSB. The LPF bandwidth must pass the full message but reject the doubled-carrier product. Gain/phase imbalance, LO leakage, DC offset and finite carrier-recovery bandwidth are practical limitations. Unlike an envelope detector, which yields \(|m(t)|\) and loses DSB phase reversals, coherent detection recovers polarity and can demodulate weak suppressed-carrier signals, at the cost of synchronization circuitry.

Practice target: 16-18 minutes; derive the LPF output with both \(\phi\) and \(\Delta\omega\), then separately explain DSB fading and SSB frequency translation.

Exam-ready answer

An FM detector converts instantaneous frequency deviation into voltage. Around center frequency \(f_c\), its desired S-curve is

where \(K_D\) is detector sensitivity in volts per hertz. Output is zero at \(f_c\) and has opposite polarities above and below it.

A slope detector tunes a resonant circuit so \(f_c\) lies on one amplitude-response slope. Frequency movement becomes amplitude movement and a diode envelope detector recovers the message. It is simplest but has narrow linear range, asymmetric distortion and strong AM/noise sensitivity. A limiter is required. A balanced slope detector subtracts two opposite slopes for better symmetry.

A Foster-Seeley discriminator uses a center-tapped double-tuned transformer. Frequency deviation changes secondary phase relative to the reference; two diode voltages are equal at \(f_c\) and unequal above/below, and their difference is audio. It gives high output and very good linearity but also responds to input amplitude, so a preceding limiter is essential.

A ratio detector uses a similar transformer with reversed diode/loading arrangement and a large capacitor that holds the sum of diode voltages nearly constant. Output depends mainly on their ratio/difference, giving inherent AM rejection. A separate limiter is normally unnecessary, although output and linearity may be lower than a well-aligned Foster-Seeley detector.

In a PLL detector, the phase detector and loop filter force the VCO to track input frequency. Within lock and loop bandwidth,

so loop-filter control voltage is the recovered message. It has excellent linearity, strong amplitude immunity, wide design flexibility and easy IC integration, but must acquire/retain lock and its bandwidth must follow the highest message frequency without passing excessive noise.

The limiter removes parasitic amplitude changes before detectors whose output depends on RF amplitude; it preserves zero crossings and FM deviation. It is mandatory for slope and Foster-Seeley, largely built into the behavior of ratio detection, and usually not a separate requirement for a well-designed PLL input. For \(K_{VCO}=50\,\text{kHz/V}\) and \(\Delta f=25\,\text{kHz}\), PLL output peak is \(0.5\,\text{V}\). All detectors must cover peak deviation inside their linear/lock range; misalignment creates DC offset/distortion, and broadcast receivers add de-emphasis after detection.

Practice target: 16-18 minutes; sketch the S-curve, explain each conversion mechanism, and tabulate limiter need, linearity and main limitation.

Exam-ready answer

Digital modulators map bits to controlled carrier waveforms; receivers filter/correlate the noisy waveform, recover timing/carrier where necessary and decide the most likely symbol.

ASK/OOK: a unipolar bit \(b(t)\in\{0,1\}\) controls an RF switch or multiplier, giving \(s(t)=A_cb(t)\cos\omega_ct\). A noncoherent receiver uses BPF \(\rightarrow\) envelope detector \(\rightarrow\) matched/low-pass filter \(\rightarrow\) clocked threshold. Coherent ASK instead multiplies by a recovered carrier and integrates/correlates. OOK is simple but amplitude noise/fading directly moves its decision metric.

BFSK: bits select two tones \(f_0\) and \(f_1\) using a VCO, DDS or phase-continuous oscillator switch. A noncoherent receiver has two bandpass filters and energy/envelope detectors; it chooses the larger energy. A coherent receiver uses two synchronized correlators, while a discriminator or PLL may convert mark/space frequency to two voltages. BFSK tolerates nonlinear PAs and amplitude variation but generally uses more bandwidth than PSK.

BPSK: map bits to \(a_k=\pm1\) and drive a balanced product modulator, so carrier phase is \(0\) or \(\pi\). The coherent receiver uses carrier recovery/Costas loop \(\rightarrow\) product detector \(\rightarrow\) matched filter or integrate-and-dump \(\rightarrow\) zero-threshold decision. Differential encoding can remove the \(180^\circ\) carrier-phase ambiguity. BPSK has strong power efficiency but requires phase synchronization.

QPSK: a serial-to-parallel mapper forms I and Q symbols in \(\{\pm1\}\). Pulse-shaped branches multiply orthogonal carriers and add:

At the receiver, coherent quadrature LOs down-convert to I/Q, matched filters maximize sampled SNR, symbol-timing recovery chooses sample instants, and two sign decisions recover two bits per symbol. Gray mapping limits most nearest-neighbor errors to one bit.

Carrier recovery is essential for BPSK/QPSK; symbol timing is essential for all four, and frame/AGC/equalization may also be required. For \(R_s=1\,\text{Msymbol/s}\), BPSK carries \(1\,\text{Mbit/s}\) while QPSK carries \(2\,\text{Mbit/s}\) before coding, explaining QPSK's bandwidth efficiency. Practical filters limit occupied spectrum but introduce ISI unless matched/equalized; frequency/phase error rotates PSK decisions, while nonlinear PA operation distorts amplitude-varying signals. ASK favors simplicity, BFSK robustness/noncoherent options, BPSK power efficiency and QPSK twice the bits per symbol.

Practice target: 17-19 minutes; draw each modulator/detector path, distinguish coherent from noncoherent detection, and state all synchronization needs.