Why does impedance mismatch waste power?

When the load impedance differs from the source impedance, part of the incident power reflects back toward the source. The reflected power is not absorbed by the load and is either dissipated in the source's output resistance or re-reflected, creating standing waves. The fraction of reflected power is the square of the reflection coefficient: P_reflected = |gamma|^2 times P_incident. At VSWR 2.0, 11% of the power is reflected. At VSWR 3.0, 25% is reflected. An impedance matching network transforms the load impedance to the source's conjugate, making gamma zero and delivering 100% of available power.

What determines matching network bandwidth?

The Bode-Fano limit sets the theoretical maximum bandwidth for matching a reactive load. For a parallel RC load: the integral of ln(1/|gamma|) over all frequencies cannot exceed pi/(R times C). This means you can have a perfect match at one frequency (narrowband) or an imperfect match over a wide band, but not both. The quality factor Q of the matching network quantifies this trade-off: Q = f0/BW. An L-network has a fixed Q determined by the impedance ratio: Q = sqrt(R_high/R_low - 1). For a 10:1 transformation (50 to 5 ohms), Q = 3.0, giving about 33% fractional bandwidth.

When should I use Pi or T networks instead of an L-network?

An L-network has only two components and its Q is fixed by the impedance ratio, giving no control over bandwidth. A Pi network (three components) adds one degree of freedom, allowing you to choose the Q independently of the impedance ratio. Higher Q gives a narrower, sharper match with better out-of-band rejection (useful for harmonic filtering). Lower Q gives broader bandwidth. A T network also has three components but creates a high-impedance virtual node that is useful for matching two low impedances. Pi networks are preferred at PA outputs (they provide harmonic filtering), while T networks are common at LNA inputs.

RF Design

Impedance Matching

A GaN power transistor's optimal load impedance at 3.5 GHz is 2.3 + j4.1 Ω. The antenna system is 50 Ω. Without a matching network between them, 90% of the power bounces back into the transistor as heat. Two capacitors and an inductor, chosen with the right values and arranged in the right topology, transform the 50 Ω load into the 2.3 + j4.1 Ω the transistor needs to deliver its rated power. That is impedance matching: the art of making two different impedances look identical to each other so that maximum power transfers between them.

Category: RF Design

Goal: Γ = 0 (zero reflection)

Tool: Smith Chart

Network Topologies and Their Trade-offs

Topology	Components	Q Control	Bandwidth	Harmonic Filtering	Best Application
L-network	2 (L + C)	Fixed by Z ratio	Moderate	None	Simple matching, low ratio
Pi-network	3 (C-L-C)	Selectable	Adjustable	Good (lowpass form)	PA output, harmonic suppression
T-network	3 (L-C-L)	Selectable	Adjustable	Poor	LNA input, high-Z nodes
Quarter-wave TL	1 (line section)	Fixed (~4)	~20%	None	Microstrip, >1 GHz
Multi-section transformer	2 to 5 sections	Low	Octave+	None	Broadband, Chebyshev taper

L-network design (R_S > R_L):
Q = √(R_S/R_L − 1)
X_series = Q × R_L
X_shunt = R_S / Q

Example: 50 Ω to 5 Ω at 2 GHz:
Q = √(50/5 − 1) = √9 = 3.0
X_series = 3 × 5 = 15 Ω → L = 15/(2π×2×10⁹) = 1.19 nH
X_shunt = 50/3 = 16.7 Ω → C = 1/(2π×2×10⁹×16.7) = 4.77 pF
BW ≈ f₀/Q = 2 GHz/3 = 667 MHz (33% fractional)

Practical Design Considerations

On a PCB above 2 GHz, lumped inductors have self-resonant frequencies that limit usable values to a few nanohenries. Capacitors above 10 pF become inductive before reaching the operating frequency. Designers increasingly replace lumped components with microstrip stubs and line sections that behave as distributed inductors and capacitors. A high-impedance line section acts as a series inductor; a low-impedance section acts as a shunt capacitor. At millimeter-wave frequencies (28 GHz and above), all matching is done with transmission line segments because no practical lumped components exist. Component Q also matters: a matching network with component Q of 50 adds about 0.2 dB of insertion loss for a 10:1 impedance transformation, while a Q of 20 adds 0.5 dB. This dissipative loss directly reduces PA output power or receiver sensitivity.

Common Questions

Frequently Asked Questions

Why does mismatch waste power?

Mismatched impedance causes reflection: |Γ|² of the incident power bounces back. At VSWR 2.0: 11% reflected. At VSWR 3.0: 25% reflected. A matching network makes Γ = 0, delivering 100% of available power to the load.

What determines bandwidth?

The Bode-Fano limit: perfect match at one frequency or imperfect match over a band, never both. L-network Q = √(R_high/R_low − 1) is fixed. For 10:1 ratio: Q = 3, BW = 33%. Pi/T networks allow independent Q selection.

When Pi or T instead of L?

L-network: fixed Q, 2 components, no harmonic filtering. Pi: selectable Q, lowpass form provides harmonic suppression (ideal for PA output). T: selectable Q, high-Z virtual node (useful for LNA input matching between low impedances).

Related Terms

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Design Tools

Matching Network Synthesizer

Enter source and load impedance, frequency, and choose L, Pi, or T topology. Get component values, Smith Chart plot, and bandwidth estimate.

Design a Match