Modulation Modulation
Modulation encodes information onto a carrier signal by varying its amplitude (AM), frequency (FM), or phase (PM). Analog methods include AM (simple but noise-prone) and FM (noise-resistant, used in FM radio). Digital methods include ASK, FSK, PSK, and QAM (combines AM and PM for high data rates). Wi-Fi uses 256-QAM or higher, encoding 8+ bits per symbol. The choice balances data rate, bandwidth efficiency, noise resistance, and hardware complexity.
Why We Need Modulation
Baseband signals (voice at 300-3400 Hz, data as digital pulses) cannot be transmitted efficiently through the air. Antennas must be a significant fraction of the wavelength — a 3 kHz audio signal would need a 100 km antenna. Modulation shifts information to a higher carrier frequency where antennas are practical (100 MHz FM carrier needs a 1.5 m antenna). Modulation also enables frequency division multiplexing — each radio station uses a different carrier frequency, coexisting without interference.
Key Formulas
Analog Modulation: AM, FM, and PM
Amplitude Modulation (AM) varies carrier amplitude proportionally to the message: s(t) = [1 + m·x(t)]cos(2πf_ct). AM is simple but wastes power and is noise-susceptible. Frequency Modulation (FM) varies carrier frequency: instantaneous frequency = f_c + k_f·x(t). FM provides better noise immunity because noise primarily affects amplitude, which FM receivers ignore. The tradeoff is wider bandwidth — FM channels are 200 kHz wide versus 10 kHz for AM. Phase Modulation (PM) is mathematically related to FM, varying instantaneous phase rather than frequency.
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Open CalculatorDigital Modulation: ASK, FSK, PSK, and QAM
Digital modulation maps bits to carrier variations. ASK switches between amplitude levels — simplest but most noise-sensitive. FSK switches between frequencies — used in Bluetooth and early modems. PSK switches between phase angles — BPSK uses 2 phases (1 bit/symbol), QPSK uses 4 (2 bits/symbol). QAM combines amplitude and phase — 16-QAM encodes 4 bits per symbol, 256-QAM encodes 8 bits per symbol. Higher-order QAM increases data rate but requires better signal-to-noise ratio.
Bandwidth Efficiency and the Shannon Limit
Shannon's channel capacity theorem: C = B·log₂(1 + SNR) sets the absolute data rate limit. Higher-order modulation increases spectral efficiency but requires higher SNR. 256-QAM achieves 8 bits/Hz but needs about 30 dB SNR, while BPSK achieves 1 bit/Hz but works at 0 dB SNR. Modern 5G and Wi-Fi 6 adaptively switch modulation order based on channel conditions — using high-order QAM when the signal is strong and falling back to robust BPSK when it's weak.
Modulation and the Frequency Domain
Modulation is fundamentally a frequency-domain operation. AM multiplies message by carrier — by the convolution theorem, this shifts the message spectrum to the carrier frequency, creating sidebands. FM creates multiple sidebands whose amplitudes follow Bessel functions. The Laplace transform analyzes modulation circuits: AM modulators, FM demodulators, and phase-locked loops all have transfer functions analyzable with Laplace methods. The LAPLACE Calculator can help analyze these circuits.
Related Topics in signal processing techniques
Understanding modulation modulation connects to several related concepts: what is modulation, what is modulation of signal, types of modulation, and types of signal modulation. Each builds on the mathematical foundations covered in this guide.
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