Electronics Guide

Why RF Is Different

Several factors distinguish RF circuit design from low-frequency electronics:

• Wavelength effects: When circuit dimensions approach a significant fraction of wavelength, distributed effects become important.
• Parasitic elements: Stray inductance and capacitance that are negligible at low frequencies become dominant at RF.
• Impedance matching: Maximum power transfer requires careful impedance matching throughout the signal path.
• Transmission lines: Interconnects behave as transmission lines with characteristic impedance.
• Radiation: Circuits can unintentionally radiate or receive electromagnetic energy.
• Skin effect: Current flows primarily on conductor surfaces, increasing effective resistance.

S-Parameters

Scattering parameters (S-parameters) characterize RF networks by relating incident and reflected waves at each port. For a two-port network:

• S11: Input reflection coefficient (return loss at port 1).
• S21: Forward transmission (gain or insertion loss).
• S12: Reverse transmission (isolation).
• S22: Output reflection coefficient (return loss at port 2).

S-parameters are measured with reference to a system impedance (usually 50 ohms) and enable cascading of network responses using matrix multiplication.

The Smith Chart

The Smith chart is a graphical tool for visualizing complex impedances and designing matching networks. Key features:

• Constant resistance circles
• Constant reactance arcs
• Constant VSWR circles centered at chart center
• Movement along transmission lines traces arcs toward the center or periphery

Adding series or shunt elements moves impedance along predictable paths, enabling intuitive matching network design.

Transmission Lines

At RF, interconnects are transmission lines characterized by:

• Characteristic impedance (Z0): Ratio of voltage to current for traveling waves.
• Propagation constant: Describes phase shift and attenuation per unit length.
• Velocity factor: Speed of propagation relative to light speed in vacuum.

Common transmission line types include coaxial cable, microstrip, stripline, and coplanar waveguide. Impedance discontinuities cause reflections characterized by voltage standing wave ratio (VSWR).

Low-Noise Amplifiers (LNAs)

LNAs form the first active stage in receivers, where noise performance is critical. Design considerations include:

• Noise figure: Measure of noise added by the amplifier, ideally close to device minimum.
• Input matching: Match for noise (not always same as match for gain) or compromise.
• Gain: Sufficient gain to overcome subsequent stage noise contributions.
• Linearity: Handle desired and interfering signals without distortion.
• Stability: Unconditional stability prevents oscillation with any load.

Common topologies include common-source/common-emitter with inductive degeneration for simultaneous noise and input match, cascode for improved isolation and bandwidth, and differential designs for common-mode rejection.

Power Amplifiers (PAs)

PAs deliver required output power to antennas. Key specifications:

• Output power: Peak and average power capability.
• Efficiency: Power added efficiency (PAE) relates RF output to DC consumption.
• Linearity: Intermodulation distortion, ACPR (adjacent channel power ratio), EVM (error vector magnitude).
• Operating class: Class A (linear, ~25% max efficiency), Class AB (compromise), Class B (50% max), Class C (high efficiency, non-linear), switch-mode classes (D, E, F).

Modern PA techniques include:

• Doherty: Load modulation improves efficiency at backed-off power.
• Envelope tracking: Varying supply voltage matches envelope, improving efficiency.
• Digital pre-distortion (DPD): Compensates PA nonlinearity to meet spectral requirements.
• Outphasing: Combines constant-envelope signals for efficient linear amplification.

Variable Gain Amplifiers

VGAs provide controllable gain for automatic gain control (AGC) systems. Implementations include:

• Variable bias current amplifiers
• Gilbert cell-based designs
• Switched attenuator banks
• Variable feedback networks

Amplifier Stability

RF amplifiers can oscillate if stability criteria are not met. The Rollett stability factor (K) and auxiliary conditions determine stability:

• K > 1 and |Delta| < 1: Unconditionally stable.
• K < 1: Potentially unstable for some source/load impedances.

Stabilization techniques include resistive loading (reduces gain), feedback networks, and careful source/load impedance control.

Oscillator Fundamentals

Oscillators require a feedback loop with unity loop gain and zero phase shift at the oscillation frequency. The Barkhausen criteria establish oscillation conditions. Oscillator types include:

• LC oscillators: Colpitts, Hartley, Clapp configurations using inductors and capacitors.
• Crystal oscillators: High stability using piezoelectric resonators.
• Dielectric resonator oscillators (DROs): High-Q resonators for microwave frequencies.
• YIG oscillators: Wideband tunable using yttrium iron garnet resonators.
• Ring oscillators: Delay element chains, common in integrated circuits.

Phase Noise

Phase noise describes short-term frequency instability as noise sidebands around the carrier. Specified in dBc/Hz at offset frequencies, phase noise affects:

• Receiver sensitivity through reciprocal mixing
• Transmitter spectral purity
• Data demodulation accuracy
• Radar performance

Low phase noise requires high-Q resonators, low-noise active devices, and careful design of bias and feedback networks.

Voltage-Controlled Oscillators (VCOs)

VCOs tune frequency with a control voltage, essential for frequency synthesis. Key specifications:

• Tuning range: Frequency span over control voltage range.
• Tuning sensitivity (Kvco): Hz/V gain.
• Phase noise: Typically worse than fixed-frequency oscillators.
• Pushing/pulling: Frequency sensitivity to supply voltage and load changes.

Varactor diodes provide tuning by varying capacitance with applied voltage.

Phase-Locked Loops (PLLs)

PLLs lock VCO frequency to a reference, enabling precise frequency synthesis:

• Reference oscillator: Stable crystal oscillator as frequency standard.
• Phase detector: Compares reference and VCO phases.
• Loop filter: Integrates error signal, determines loop dynamics.
• Frequency divider: Enables synthesis of frequencies that are multiples of reference.

Fractional-N PLLs use sigma-delta modulators to synthesize non-integer frequency ratios with fine resolution. Integer-N PLLs have simpler design but coarser step size.

Direct Digital Synthesis (DDS)

DDS generates waveforms from digital representations, offering fast frequency switching and fine resolution. A phase accumulator increments at each clock cycle, addressing a lookup table for waveform samples, followed by DAC conversion and filtering.

Mixer Fundamentals

Mixers multiply two signals, producing sum and difference frequencies. In receivers, mixers downconvert RF to IF; in transmitters, they upconvert baseband to RF. Ideal mixer output contains:

• Desired frequency component (sum or difference)
• Image frequency component
• LO and RF feedthrough
• Intermodulation products

Mixer Types

• Diode mixers: Simple, passive, broadband. Single-balanced rejects LO from output; double-balanced rejects both LO and RF feedthrough.
• Gilbert cell: Active mixer providing conversion gain, common in integrated circuits.
• Passive FET mixers: Low distortion using FETs as switches.
• Harmonic mixers: Use LO harmonics for conversion to higher frequencies.
• Sub-harmonic mixers: Use lower frequency LO, useful when LO generation is challenging.

Mixer Specifications

• Conversion loss/gain: Ratio of IF power to RF power.
• Noise figure: Noise contribution of the mixer.
• Port-to-port isolation: LO-RF, LO-IF, RF-IF isolation.
• IP3: Third-order intercept point indicating linearity.
• P1dB: 1 dB compression point.
• LO drive level: Required local oscillator power.

Image Rejection

Superheterodyne receivers produce responses at both RF and image frequencies (RF +/- 2*IF from desired). Image rejection techniques include:

• RF filtering: Preselection filter attenuates image.
• Image-reject mixers: Weaver or Hartley architectures using quadrature mixing.
• High IF: Places image farther from desired, easier to filter.
• Dual conversion: Multiple IF stages with filtering at each.

Filter Types

Filters select desired frequencies while rejecting others:

• Low-pass: Pass frequencies below cutoff.
• High-pass: Pass frequencies above cutoff.
• Band-pass: Pass frequencies within a band.
• Band-stop (notch): Reject frequencies within a band.

Filter Responses

• Butterworth: Maximally flat passband, gentle rolloff.
• Chebyshev: Steeper rolloff with passband ripple.
• Elliptic (Cauer): Steepest rolloff with both passband and stopband ripple.
• Bessel: Linear phase (constant group delay) for minimal signal distortion.
• Gaussian: Optimized time-domain response for minimum overshoot.

Filter Implementation Technologies

• Lumped element: Discrete inductors and capacitors, practical at lower RF frequencies.
• Distributed element: Transmission line sections at microwave frequencies.
• SAW (Surface Acoustic Wave): Compact, highly selective filters using acoustic waves on piezoelectric substrates.
• BAW (Bulk Acoustic Wave): Similar to SAW but using bulk resonance, better power handling.
• Cavity filters: High-Q resonant cavities for base stations and high-power applications.
• Dielectric resonator filters: High-Q, temperature-stable microwave filters.
• Active filters: Use amplifiers to achieve filtering, enabling integration.

Filter Specifications

• Passband insertion loss: Loss in the passband.
• Stopband rejection: Attenuation of rejected frequencies.
• Bandwidth: Width of passband (often at -3 dB points).
• Shape factor: Ratio of stopband to passband widths.
• Return loss: Impedance match quality.
• Group delay: Variation causes signal distortion.
• Power handling: Maximum RF power capacity.

Why Match?

Impedance matching maximizes power transfer and minimizes reflections. Mismatch causes:

• Reduced power delivery to load
• Standing waves on transmission lines
• Increased line losses
• Potential damage to power amplifiers
• Distortion from multiple reflections

Matching Network Topologies

• L-network: Two elements (inductor and capacitor), simplest but narrowband.
• Pi-network: Three elements, more flexibility in Q factor.
• T-network: Three elements, alternative to pi.
• Quarter-wave transformer: Transmission line section for real-to-real transformation.
• Stub matching: Open or shorted transmission line stubs.
• Multi-section matching: Cascaded sections for broadband matching.

Broadband Matching

Wideband matching uses multiple sections or more complex networks. The Bode-Fano criterion establishes theoretical limits on matching bandwidth for a given load Q factor. Techniques include:

• Multi-section transformers (binomial, Chebyshev)
• Real frequency techniques
• Resistive matching (trades gain for bandwidth)
• Feedback (in active circuits)

Substrate Selection

PCB material properties significantly affect RF performance:

• Dielectric constant (Er): Affects trace width for desired impedance and physical size.
• Loss tangent: Determines dielectric losses; lower is better.
• Thermal properties: Coefficient of thermal expansion, thermal conductivity.
• Common materials: FR-4 (economical, higher loss), Rogers (low loss), ceramic (specialized applications).

Transmission Line Implementation

PCB transmission line types:

• Microstrip: Trace on top layer over ground plane. Simple but exposed to environment.
• Stripline: Trace between two ground planes. Better shielding but harder to interface.
• Coplanar waveguide: Ground planes adjacent to trace on same layer. Good for probing and component mounting.
• Grounded CPW: CPW with additional ground plane below.

Layout Practices

• Controlled impedance: Maintain consistent trace width and spacing.
• Via placement: Ground vias near signal transitions, via fences for isolation.
• Component placement: Minimize path lengths, separate high-power from sensitive circuits.
• Decoupling: Capacitors close to power pins with low-inductance connections.
• Shielding: Ground pours, fence vias, and compartmentalization.
• Thermal management: Heat spreading for power devices.

Superheterodyne

Classic architecture converting RF to fixed IF for filtering and processing. Benefits include high selectivity and dynamic range. Drawbacks include image response and multiple conversion stages for complex systems.

Direct Conversion

Converts directly to baseband, eliminating IF stages. Advantages include simpler architecture and easier integration. Challenges include DC offset, flicker noise, and I/Q imbalance.

Low-IF

Converts to low IF (hundreds of kHz to few MHz), combining benefits of both architectures. Avoids DC issues while maintaining simple filtering.

Digital IF and Software-Defined Radio

Digitize at IF or RF, performing frequency conversion and processing in digital domain. Maximum flexibility but requires high-performance ADCs/DACs and significant processing power.

Circuit Simulation

RF simulators model high-frequency behavior:

• Linear simulation: S-parameter analysis for cascaded networks.
• Harmonic balance: Nonlinear steady-state analysis for mixers, oscillators, PAs.
• Transient simulation: Time-domain analysis for startup behavior, modulated signals.
• Electromagnetic simulation: 2D and 3D field solvers for passive structures.

Test Equipment

• Vector network analyzer: Measures S-parameters, impedance.
• Spectrum analyzer: Displays power versus frequency.
• Signal generator: Produces test signals.
• Power meter: Accurate power measurement.
• Noise figure analyzer: Measures receiver noise performance.