Basics

The relationship is defined by Ohm’s Law: V = IZ. In an AC circuit, impedance Z is frequency-dependent and includes resistive (R) and reactive (X) components: Z = R + jX.

As frequency changes, the reactive components vary significantly:

• Inductive reactance: X_L = 2πfL — increases with frequency
• Capacitive reactance: X_C = 1/(2πfC) — decreases with frequency

This alters the overall impedance magnitude and phase angle at different operating frequencies.

When source and load impedances are mismatched, maximum power transfer does not occur due to reflections at the interface. A portion of the power is reflected back to the source, lowering efficiency and potentially damaging the source in high-power systems.

Maximum power transfer occurs when Z_L = Z_S* (conjugate match). The reflection coefficient quantifies the mismatch:

Two common approaches:

• L-network (lumped element): Use a series inductor and shunt capacitor (or vice versa) to transform 75Ω to 50Ω. The Q-factor determines component values: Q = √(75/50 − 1) ≈ 0.707.
• Quarter-wave transformer (distributed): Use a transmission line with characteristic impedance:

The L-network is compact for lumped designs; the quarter-wave transformer is better for PCB/microstrip implementations.

ACR (Attenuation to Crosstalk Ratio) is the difference between signal attenuation and crosstalk levels in a communication system. High ACR ensures that signal integrity is maintained, which is critical for minimizing interference and maximizing data transmission quality in RF systems.

Inductive reactance (X_L = 2πfL) increases linearly with frequency, while capacitive reactance (X_C = 1/(2πfC)) decreases inversely.

At low frequencies, capacitors dominate impedance. At high frequencies, inductors dominate. At resonance (X_L = X_C), the reactive components cancel, leaving only resistance.

At higher frequencies, the skin effect causes current to concentrate near the surface of the conductor, reducing the effective cross-sectional area for current flow. The skin depth is:

This increases the AC resistance, leading to higher losses. At microwave frequencies, the skin depth in copper is only a few micrometers, meaning surface roughness and plating quality significantly impact performance.

The dielectric material determines the permittivity (ε_r) of the PCB, affecting:

• Signal velocity: v = c/√ε_r — higher ε_r means slower propagation
• Characteristic impedance: Higher ε_r reduces Z₀ for a given trace geometry
• Dielectric losses: Higher loss tangent (tanδ) means more signal attenuation at higher frequencies

This is why low-loss materials (Rogers, Megtron) are used for RF boards instead of standard FR-4.

An open-ended transmission line has infinite impedance at the termination, meaning no current flows into it. The boundary condition requires current to be zero at the open end. Since power cannot be dissipated (no load), all incident energy must reflect back.

This means total reflection with no phase inversion.

In a capacitive element, the current leads the voltage by 90 degrees (phase advance). In an inductive element, the current lags the voltage by 90 degrees (phase delay).

1. Measure the line’s VSWR or return loss using a network analyzer to identify impedance mismatches and their locations (via TDR).
2. Inspect for physical damage — bent connectors, damaged cables, cold solder joints.
3. Analyze for crosstalk or EMI issues from adjacent traces or external sources.
4. Verify insertion loss vs. frequency to distinguish conductor loss, dielectric loss, and radiation loss.
5. Adjust matching network or replace damaged components as needed.

Start by reviewing the system’s design, including filter characteristics and impedance matching. Measure S-parameters end-to-end and per stage to identify unexpected resonances or losses. Evaluate components for nonlinearities or parasitic effects. Check if PCB parasitics (via inductance, trace capacitance) are creating unintended frequency-dependent behavior. Verify that component models used in simulation accurately represent the physical parts.

0 dBm = 1 milliwatt (mW), or 0.001 W. The dBm scale is defined as power relative to 1 mW:

A power splitter divides an input signal into two (or more) output signals. In an ideal lossless 2-way splitter, each output receives half the input power, which is a 3 dB reduction per port. Real splitters also have insertion loss (typically 0.1–0.5 dB additional).

Where:

• kTB: Thermal noise floor = −174 dBm/Hz + 10·log(BW) — the fundamental noise power in a given bandwidth
• NF: System noise figure — how much noise the receiver adds
• SNR_min: Minimum signal-to-noise ratio required for the modulation scheme to achieve the target BER

In free space, Maxwell’s equations show that time-varying electric fields create magnetic fields and vice versa, enabling self-sustaining TEM wave propagation in any direction at the speed of light.

In a waveguide, conducting boundary conditions constrain the fields. Only specific field configurations (TE, TM modes) can propagate, each with a cutoff frequency below which propagation is not supported. The waveguide acts as a high-pass filter, and the phase velocity is always greater than c while the group velocity is less than c.