3.4 Microstrip transmission lines

Microstrip Transmission Line Structure

A microstrip transmission line is one of the most common planar structures in microwave circuit design. It consists of three parts: a conductor strip on top, a dielectric substrate in the middle, and a ground plane on the bottom. The geometry and material properties of these three layers determine the line's electrical behavior.

Conductor Strip

The conductor strip is a thin, flat metal trace (usually copper) that carries the signal. Its width and thickness directly control two things: the characteristic impedance and the current-carrying capacity. A wider strip lowers the characteristic impedance and allows more current to flow.

Dielectric Substrate

The substrate is an insulating layer that separates the conductor strip from the ground plane. Common materials include FR-4 (cheap, used at lower frequencies), Rogers laminates (low loss, used at microwave frequencies), and alumina (ceramic, high dielectric constant).

Two substrate properties matter most:

• Dielectric constant ($\varepsilon_r$): affects impedance, phase velocity, and field confinement
• Loss tangent ($\tan \delta$): determines how much energy the substrate absorbs

A thicker substrate with a lower $\varepsilon_r$ gives higher impedance and wider traces, while a thinner substrate with higher $\varepsilon_r$ gives lower impedance and narrower traces.

Ground Plane

The ground plane is a continuous conductive layer (typically copper) beneath the substrate. It serves as the return path for current and the reference for the electromagnetic fields. It also helps confine fields within the substrate, reducing radiation losses.

Microstrip Line vs. Stripline

Both microstrip and stripline are planar transmission line structures, but they differ in geometry, field behavior, and mode purity.

Geometry Differences

• Microstrip: open structure with the conductor on top of one substrate layer and a single ground plane below. Fields extend partly into the air above.
• Stripline: enclosed structure with the conductor sandwiched between two substrate layers and two ground planes. Fields are fully contained.

Because of its open structure, microstrip is more susceptible to external interference and radiation losses. Stripline provides better shielding but is harder to fabricate and doesn't allow easy access to mount surface components.

Field Distribution

In a stripline, the dielectric environment is homogeneous (same material above and below the conductor), so it supports a pure TEM mode. In a microstrip, part of the field travels through the substrate and part through air. This inhomogeneous environment means the mode is not purely TEM. Instead, small longitudinal field components exist, and the mode is called quasi-TEM.

Quasi-TEM Mode of Propagation

The open, inhomogeneous dielectric environment of a microstrip line prevents it from supporting a true TEM mode. The result is a quasi-TEM mode with important practical consequences.

Non-Pure TEM Mode

In a pure TEM mode, electric and magnetic fields are entirely transverse (perpendicular to the propagation direction). In microstrip, because the fields split between the substrate ($\varepsilon_r > 1$) and air ($\varepsilon_r = 1$), small longitudinal components appear.

This causes dispersion: the phase velocity and characteristic impedance become frequency-dependent. At low frequencies the quasi-TEM approximation works well, but at higher frequencies dispersion becomes significant and full-wave analysis may be needed.

Effective Dielectric Constant

To handle the mixed dielectric environment within the quasi-TEM framework, an effective dielectric constant ($\varepsilon_{eff}$) is introduced. It represents a weighted average of the substrate and air dielectric constants, accounting for how much of the field energy resides in each region.

$\varepsilon_{eff}$ always satisfies:

$1 < \varepsilon_{eff} < \varepsilon_r$

and is typically closer to $\varepsilon_r$ because most of the field energy is concentrated in the substrate. A wider strip confines more field in the substrate, pushing $\varepsilon_{eff}$ closer to $\varepsilon_r$. A narrower strip lets more field fringe into the air, lowering $\varepsilon_{eff}$.

The phase velocity on the line is then:

$v_p = \frac{c}{\sqrt{\varepsilon_{eff}}}$

where $c$ is the speed of light in vacuum.

Characteristic Impedance of Microstrip Lines

The characteristic impedance ($Z_0$) governs how signals reflect and transmit at interfaces and discontinuities. Getting $Z_0$ right is fundamental to impedance matching in any microwave circuit.

Impedance Formula

One commonly used approximate formula (valid for $w/h \leq 2$) is:

$Z_0 = \frac{87}{\sqrt{\varepsilon_r + 1.41}} \ln \left(\frac{5.98h}{0.8w + t}\right)$

where:

• $\varepsilon_r$ = substrate dielectric constant
• $h$ = substrate thickness
• $w$ = conductor strip width
• $t$ = conductor strip thickness

Note that more accurate closed-form expressions exist (such as those by Hammerstad and Jensen) that cover both narrow and wide strip regimes. For precise designs, electromagnetic simulators are typically used.

Width-to-Height Ratio

The ratio $w/h$ is the primary geometric knob for setting impedance:

• Large $w/h$ (wide strip, thin substrate) → lower $Z_0$
• Small $w/h$ (narrow strip, thick substrate) → higher $Z_0$

Practical microstrip impedances typically range from about 20 Ω to 120 Ω, with 50 Ω being the standard for most RF systems.

Dielectric Constant Impact

For a fixed $w/h$, a higher $\varepsilon_r$ lowers $Z_0$. This means that on a high-$\varepsilon_r$ substrate (like alumina, $\varepsilon_r \approx 9.8$), you need a narrower strip to achieve 50 Ω compared to a low-$\varepsilon_r$ substrate (like Rogers RO4003, $\varepsilon_r \approx 3.55$). Lower-$\varepsilon_r$ substrates also tend to have lower dispersion and wider traces, which can reduce conductor losses.

Microstrip Line Losses

Three loss mechanisms limit microstrip performance, and all of them get worse at higher frequencies.

Conductor Losses

These arise from the finite conductivity of the metal traces. As frequency increases, the skin effect forces current to flow in an increasingly thin layer at the conductor surface, raising the effective resistance. You can reduce conductor losses by:

• Using high-conductivity metals (copper, gold)
• Increasing conductor thickness (up to several skin depths)
• Using wider traces (lower current density)

Dielectric Losses

Energy is dissipated in the substrate due to polarization losses in the dielectric material. The loss tangent $\tan \delta$ quantifies this. For example, FR-4 has $\tan \delta \approx 0.02$, while Rogers RO4350B has $\tan \delta \approx 0.004$. At microwave frequencies, substrate choice matters a lot.

Radiation Losses

The open structure of microstrip means some energy radiates away, especially at discontinuities (bends, open ends, junctions) and at higher frequencies. Using a higher-$\varepsilon_r$ substrate confines the fields more tightly and reduces radiation. Thinner substrates also help, though they increase conductor losses for a given impedance.

Microstrip Discontinuities

Any abrupt change in microstrip geometry creates a discontinuity that scatters energy, causing reflections and parasitic reactive effects. Good microwave design requires understanding and compensating for these.

Steps in Width

When the conductor width changes abruptly, the junction introduces parasitic reactance:

• A step to a wider line adds excess capacitance (field fringing at the wider section)
• A step to a narrower line adds excess inductance

Compensation techniques include chamfering (cutting a notch at the step) or tapering (gradually transitioning the width) to reduce reflections.

Bends and Corners

Right-angle bends are common in circuit layouts but introduce excess capacitance at the outer corner where charge accumulates. Two standard fixes:

• Mitered bends: the outer corner is chamfered (typically at 45°), removing the excess capacitance. An optimal miter removes about 50–70% of the corner area.
• Curved bends: using a gradual curve with a radius of at least 3× the strip width minimizes reflections.

T-Junctions

A T-junction forms where three microstrip lines meet, used for power dividers, combiners, and switching networks. The junction itself introduces parasitic reactance that causes mismatch. Matching techniques include:

• Quarter-wave transformers at the junction arms
• Reactive stubs to cancel the junction's parasitic susceptance
• Adjusting the reference plane positions in the design

Microstrip Coupled Lines

When two microstrip traces run parallel and close together on the same substrate, their fields overlap and they become electromagnetically coupled. This coupling is the basis for directional couplers, filters, and other components.

Even and Odd Mode Impedances

The coupled system supports two fundamental modes:

• Even mode: currents flow in the same direction on both lines. The symmetry plane between the lines acts like a magnetic wall (open circuit). This mode has characteristic impedance $Z_{0e}$.
• Odd mode: currents flow in opposite directions. The symmetry plane acts like an electric wall (short circuit). This mode has characteristic impedance $Z_{0o}$.

$Z_{0e} > Z_{0o}$ always, and both depend on the strip widths, the gap between the strips, and the substrate properties. The uncoupled (single-line) impedance $Z_0$ is related to these by $Z_0 = \sqrt{Z_{0e} \cdot Z_{0o}}$.

Coupling Coefficient

The coupling coefficient $k$ quantifies how strongly the two lines interact:

$k = \frac{Z_{0e} - Z_{0o}}{Z_{0e} + Z_{0o}}$

• Tight coupling ($k$ close to 1): lines are very close together, large difference between $Z_{0e}$ and $Z_{0o}$
• Loose coupling ($k$ close to 0): lines are far apart, $Z_{0e} \approx Z_{0o}$

For a typical edge-coupled microstrip coupler, achieving coupling tighter than about $-8$ dB is difficult because the required gap becomes impractically small. Broadside-coupled or Lange couplers are used when tighter coupling is needed.

Microstrip Filters

Microstrip filters are passive structures that pass or reject signals based on frequency. They replace bulky waveguide or lumped-element filters in planar microwave circuits.

Low-Pass Filters

These pass signals below a cutoff frequency and attenuate higher frequencies. Common microstrip implementations:

• Stepped-impedance: alternating sections of high-$Z_0$ (narrow, series inductance) and low-$Z_0$ (wide, shunt capacitance) lines
• Stub-based: open or shorted stubs that present reactive loading at specific frequencies

The filter order (number of reactive elements) controls the roll-off steepness. Standard prototype responses (Butterworth, Chebyshev) are used to determine the impedance values and electrical lengths of each section.

High-Pass Filters

These pass signals above a cutoff frequency. In microstrip, they're harder to realize in distributed form because a series capacitance (needed for high-pass behavior) requires gaps or interdigital structures. Designs often use coupled-line sections or lumped capacitor chips in combination with microstrip inductors.

Bandpass Filters

These pass a band of frequencies and reject everything outside it. Popular microstrip topologies include:

• Parallel-coupled (edge-coupled) filters: half-wavelength resonators coupled along their edges. The coupling gaps set the bandwidth.
• Hairpin filters: folded versions of parallel-coupled filters that save space.
• Interdigital and combline filters: used for wider bandwidths or more compact layouts.

Key design parameters are the center frequency, fractional bandwidth, and the number of resonator sections (which determines selectivity and insertion loss).

Microstrip Patch Antennas

Microstrip patch antennas are flat, low-profile radiators built on the same substrate technology as microstrip lines. They're popular in wireless systems because they're lightweight, conformal, and easy to fabricate in arrays.

Rectangular Patch

The most common geometry. The patch length $L$ is approximately half a guided wavelength at the operating frequency:

$L \approx \frac{c}{2f\sqrt{\varepsilon_{eff}}}$

The patch width $W$ affects the radiation efficiency and input impedance. A wider patch radiates more efficiently and has a lower input resistance at resonance. Typical bandwidths for a single rectangular patch are 1–5%, which is one of their main limitations.

Circular Patch

A circular patch operates on similar principles but uses a disk geometry. The fundamental mode ($TM_{110}$) radius determines the resonant frequency. Circular patches can more easily produce circular polarization by exciting two orthogonal degenerate modes with a 90° phase difference.

Feeding Techniques

How you excite the patch affects impedance matching, bandwidth, and spurious radiation:

• Microstrip line feed: a trace connects directly to the patch edge. Simple to fabricate, but the feed line itself radiates and can distort the pattern.
• Coaxial probe feed: a coaxial connector passes through the substrate from below. The probe position on the patch controls the input impedance. Good for thicker substrates but introduces probe inductance.
• Aperture coupling: a microstrip feed line on a separate layer couples to the patch through a slot in the ground plane. This provides good isolation between the feed network and the radiating element and supports wider bandwidth.
• Proximity coupling: the feed line is on an intermediate layer and couples to the patch electromagnetically without direct contact. This also offers wider bandwidth.

Microstrip Line Applications

Microstrip technology is used wherever compact, planar, and integrable high-frequency circuits are needed.

Microwave Integrated Circuits

Microstrip lines serve as interconnects, impedance-matching networks, and distributed circuit elements (replacing lumped inductors and capacitors at microwave frequencies) in MICs. They integrate directly with active devices like transistors and diodes on the same substrate, enabling compact amplifiers, mixers, oscillators, and phase shifters.

High-Frequency PCBs

At frequencies above a few hundred MHz, controlled-impedance routing becomes critical. Microstrip traces on carefully specified substrates provide predictable impedance (typically 50 Ω) and reduced crosstalk compared to uncontrolled traces. Applications include radar systems, high-speed digital links, and RF front-end modules.

Wireless Communication Systems

Microstrip components are found throughout wireless systems, from cellular base stations to Wi-Fi routers to satellite transponders. Filters, couplers, power dividers, and patch antennas are all routinely implemented in microstrip. The technology's low profile and compatibility with standard PCB manufacturing make it well suited for mass-produced consumer devices like smartphones and IoT sensors.