Electronics Guide

Antenna Efficiency

Efficient electromagnetic radiation requires antenna dimensions comparable to the signal wavelength. Audio frequencies (20 Hz to 20 kHz) would require antennas kilometers long. By modulating audio onto a higher frequency carrier, practical antenna sizes become feasible. A 1 MHz carrier has a wavelength of 300 meters, enabling quarter-wave antennas of 75 meters, and higher frequencies allow even smaller antennas.

Frequency Division Multiplexing

Modulation enables multiple signals to share the same transmission medium by occupying different portions of the frequency spectrum. Each signal modulates a different carrier frequency, and receivers can select the desired signal while rejecting others. This principle underlies radio broadcasting, cable television, and cellular networks.

Propagation Optimization

Different frequencies propagate differently through various media. Modulation allows signals to be transmitted at frequencies optimal for the intended path, whether through the atmosphere, optical fiber, or underwater. HF frequencies can reflect off the ionosphere for long-distance communication, while microwave frequencies penetrate rain better for satellite links.

Noise and Interference Immunity

Certain modulation techniques provide inherent resistance to noise and interference. Frequency modulation offers better noise performance than amplitude modulation at the expense of bandwidth. Spread spectrum techniques distribute signals across wide bandwidths, making them resistant to narrowband interference and difficult to detect.

Modulator Architectures

Common modulator implementations include:

• Direct modulation: The information signal directly controls an oscillator or amplifier parameter.
• Indirect modulation: The signal is first converted to an intermediate form, then used to modulate the carrier.
• Quadrature modulation: Two carriers in phase quadrature (90 degrees apart) enable independent modulation of in-phase (I) and quadrature (Q) components.
• Digital modulators: Digital signal processing implements modulation mathematically, with the result converted to analog for transmission.

Amplitude Modulation (AM)

AM varies carrier amplitude in proportion to the message signal. The standard AM signal is:

s(t) = [1 + m(t)] A cos(2 pi fc t)

Where m(t) is the normalized message signal. AM produces a spectrum containing the carrier and two sidebands (upper and lower), each containing the complete message information.

AM variants include:

• DSB-FC (Double Sideband Full Carrier): Standard broadcast AM, simple to demodulate but power-inefficient.
• DSB-SC (Suppressed Carrier): Carrier removed, improving power efficiency but requiring coherent detection.
• SSB (Single Sideband): One sideband removed, halving bandwidth and improving efficiency.
• VSB (Vestigial Sideband): Partial sideband suppression, used in analog television.

Frequency Modulation (FM)

FM varies carrier frequency according to the message signal:

s(t) = A cos(2 pi fc t + 2 pi kf integral of m(t) dt)

The frequency deviation delta f is proportional to the message amplitude. FM produces a theoretically infinite spectrum of sidebands whose amplitudes depend on Bessel functions. The modulation index (ratio of frequency deviation to message frequency) determines spectral characteristics.

FM provides superior noise immunity compared to AM, particularly for large modulation indices, through the capture effect and threshold extension.

Phase Modulation (PM)

PM varies carrier phase directly with the message signal:

s(t) = A cos(2 pi fc t + kp m(t))

PM and FM are closely related since frequency is the derivative of phase. PM of a signal is equivalent to FM of its derivative. Pure analog PM is less common than FM but forms the basis for digital phase modulation techniques.

Amplitude Shift Keying (ASK)

ASK varies carrier amplitude to represent digital values. Binary ASK (on-off keying or OOK) is the simplest form, switching the carrier on and off. ASK is simple but susceptible to noise and fading affecting amplitude.

Frequency Shift Keying (FSK)

FSK switches between discrete frequencies to represent digital symbols. Binary FSK uses two frequencies; M-ary FSK uses M frequencies to encode log2(M) bits per symbol. FSK provides good noise immunity and works well with non-linear amplifiers but requires more bandwidth than PSK for equivalent data rates.

Variants include:

• Continuous-phase FSK (CPFSK): Maintains phase continuity at transitions for improved spectral efficiency.
• Minimum Shift Keying (MSK): CPFSK with modulation index 0.5, providing the minimum frequency separation for orthogonality.
• Gaussian MSK (GMSK): Gaussian filtering before modulation further reduces bandwidth, used in GSM cellular.

Phase Shift Keying (PSK)

PSK encodes information in carrier phase, keeping amplitude constant. Common forms include:

• BPSK: Two phases (0 and 180 degrees), 1 bit per symbol. Most robust but lowest spectral efficiency.
• QPSK: Four phases (0, 90, 180, 270 degrees), 2 bits per symbol. Doubles capacity over BPSK with modest increase in required signal-to-noise ratio.
• 8PSK: Eight phases, 3 bits per symbol.
• Differential PSK: Information encoded in phase changes rather than absolute phase, enabling non-coherent detection.
• Offset QPSK: Staggers I and Q transitions to reduce envelope variations.

Quadrature Amplitude Modulation (QAM)

QAM combines amplitude and phase modulation, arranging symbols in a two-dimensional constellation. Common forms include:

• 16-QAM: 16 symbols, 4 bits per symbol
• 64-QAM: 64 symbols, 6 bits per symbol
• 256-QAM: 256 symbols, 8 bits per symbol
• 1024-QAM: 1024 symbols, 10 bits per symbol

Higher-order QAM achieves greater spectral efficiency but requires better signal-to-noise ratios and more linear amplification. QAM is widely used in cable modems, digital television, and wireless LANs.

Orthogonal Frequency Division Multiplexing (OFDM)

OFDM divides a wideband channel into many narrow subcarriers, each carrying low-rate data. Key advantages include:

• Multipath resilience: Long symbol periods relative to delay spread reduce intersymbol interference.
• Spectral efficiency: Overlapping orthogonal subcarriers maximize bandwidth usage.
• Simple equalization: Each narrowband subcarrier experiences flat fading.
• Adaptive modulation: Different subcarriers can use different modulation based on channel quality.

OFDM is fundamental to WiFi (802.11a/g/n/ac/ax), LTE, 5G NR, digital television, and DSL.

Spread Spectrum Techniques

Spread spectrum modulation intentionally spreads signals across bandwidth much wider than necessary:

• Direct Sequence Spread Spectrum (DSSS): Multiplies data by high-rate spreading code, expanding bandwidth. Provides processing gain against narrowband interference.
• Frequency Hopping Spread Spectrum (FHSS): Carrier frequency changes rapidly according to pseudo-random sequence. Avoids sustained interference on any single frequency.
• Chirp Spread Spectrum: Uses linear frequency sweeps (chirps), robust against Doppler shift and multipath. Used in LoRa and some radar systems.

Coherent Detection

Coherent demodulators require a locally-generated carrier synchronized in frequency and phase with the received signal. This enables optimal detection but requires carrier recovery circuits:

• Phase-locked loops (PLLs): Track carrier phase for synchronous detection.
• Costas loops: Recover suppressed carrier for DSB-SC and PSK.
• Squaring loops: Double the signal to remove modulation, revealing carrier frequency.

Non-Coherent Detection

Non-coherent methods avoid carrier synchronization complexity:

• Envelope detection: For AM signals, a diode rectifier followed by lowpass filter extracts the envelope.
• Discriminator/limiter: For FM, converts frequency variations to amplitude variations after limiting.
• Differential detection: Compares received signal with delayed version to detect phase changes.

FM Demodulation Methods

Various circuits demodulate FM signals:

• Slope detection: Off-tuned filter converts FM to AM.
• Foster-Seeley discriminator: Phase comparison between primary and secondary windings.
• Ratio detector: Similar to discriminator with AM rejection.
• Quadrature detector: Phase comparison with shifted reference, common in ICs.
• PLL demodulator: VCO control voltage represents demodulated signal.

Digital Demodulation

Modern digital receivers typically:

1. Downconvert to intermediate frequency or baseband
2. Sample with analog-to-digital converter
3. Perform timing recovery to sample at optimal instants
4. Apply carrier recovery for coherent detection
5. Equalize channel distortions
6. Make symbol decisions (hard or soft)
7. Decode error correction codes

Digital implementation enables sophisticated algorithms including maximum likelihood sequence estimation, adaptive equalization, and iterative decoding.

Bit Error Rate (BER)

BER measures the probability of bit errors versus signal-to-noise ratio (SNR). Different modulation schemes have different BER curves:

• BPSK/QPSK have identical BER performance per bit
• Higher-order modulation requires more SNR for equivalent BER
• Coding gain improves BER at given SNR

Spectral Efficiency

Spectral efficiency measures bits per second per Hertz of bandwidth. Higher-order modulation increases spectral efficiency but requires better channel conditions. The Shannon capacity limit defines the theoretical maximum spectral efficiency for a given SNR.

Power Efficiency

Power efficiency relates to energy per bit required for acceptable error rates. Constant-envelope modulations (like FSK) allow efficient non-linear amplification, while high-order QAM requires linear amplification with inherently lower efficiency.

Peak-to-Average Power Ratio (PAPR)

PAPR indicates the ratio between peak and average signal power. High PAPR (common in OFDM) requires amplifier backoff, reducing efficiency. Techniques like clipping, coding, and selective mapping reduce PAPR.

Intersymbol Interference (ISI)

Channel bandwidth limitations and multipath cause symbols to spread into adjacent time slots. Mitigation includes:

• Equalization: Filters that compensate for channel response.
• OFDM: Long symbols reduce sensitivity to ISI.
• Guard intervals: Silence periods absorb delay spread.

Fading

Multipath propagation causes signal strength variations:

• Flat fading: Entire signal affected equally, combated by diversity techniques.
• Frequency-selective fading: Different frequencies fade independently, addressed by OFDM or equalization.
• Doppler spread: Motion causes frequency shifts, limiting coherence time.

Interference

Co-channel and adjacent channel interference degrade performance. Spread spectrum provides processing gain against narrowband interference. Adaptive nulling and interference cancellation techniques actively reject interfering signals.

Analog Implementation

Traditional modulators and demodulators use analog circuits including oscillators, mixers, filters, and amplifiers. Analog implementations remain relevant for simple systems and very high frequency applications where digital processing is impractical.

Digital Signal Processing

Modern systems implement modulation and demodulation in DSP, offering flexibility, precision, and advanced algorithms. Software-defined radio (SDR) takes this further, enabling protocol changes through software updates.

Hardware Accelerators

FPGAs and ASICs accelerate computationally intensive operations like FFT (for OFDM), filtering, and coding. These enable high data rates while maintaining energy efficiency.

Broadcasting

AM broadcasting uses DSB-FC for simple receivers. FM broadcasting provides high-fidelity audio. Digital broadcasting (DAB, DVB) uses OFDM for robustness and efficiency.

Cellular Networks

2G GSM uses GMSK. 3G CDMA uses QPSK with DSSS. 4G LTE and 5G NR use OFDM with adaptive modulation up to 256-QAM or higher.

Wireless LANs

WiFi uses OFDM with modulation from BPSK to 4096-QAM depending on channel conditions, with recent standards adding features like MU-MIMO and OFDMA.

Satellite Communications

Satellites often use PSK and APSK (Amplitude and Phase Shift Keying) with adaptive coding and modulation (ACM) to optimize throughput based on link conditions.