Microstrips: Effect of Width on Operation

William Keller

Purdue University

Abstract — At high frequencies – in the microwave range of

the electromagnetic spectrum – both circuit elements and the connecting media affect the impedance of the circuit significantly. Microstrips were developed to have more control in this respect. In this experiment we examine the effect of width of microstrips on the operation of them as the connecting medium in high frequency circuits. We conclude that the wider the microstrip in comparison to the height of the dielectric it rests upon, the better its performance in higher frequency circuits.

Index Terms — Microstrips

I. INTRODUCTION

When circuits begin working with higher frequencies

- in the microwave spectrum in this case – the wires

connecting circuit components begin to have more of an effect

on circuit operation, and must be considered in the design. To

do this, the wires – the medium connecting circuit components

– are considered to have a distributed impedance proportional

to its geometric properties, spread out over the length of them.

Microstrips have been developed as a connecting medium to

replace wires at these higher frequencies due to their efficient

operation in this frequency range.

As stated, the geometry of circuit elements and this

connecting medium become important at higher frequencies.

In this experiment we varied the width of the microstrip and

sent voltage wave pulses down it while measuring the

response. The reflected voltage wave V- was measured, along

with the time TD it took to propagate along the microstrip, the

originating voltage wave V+, as well as the geometric

dimensions of the microstrip, length L, width w, and height h

of the dielectric of the microstrip as shown in Figure 1 in the

Theory section. These measurements were then used to

calculate the reflection coefficient Γ, the characteristic

impedance of the microstrip Z0, the velocity of the wave in the

microstrip v, the attenuation of the wavelength of the wave

λ/λ0, and the effective dielectric constant εreff. These were

calculated using equations developed in [1], and supplied

below for reference. The width of the microstrip was then

compared to these important parameters of operation.

Γ = V-/V

+ (1)

Z0 = 50*(1+Γ)/(1-Γ) (2)

V = L/TD (3)

λ/λ0 = v/c (4)

εreff = (c/v)^2 (5)

A. Purpose

The purpose of this experiment was to vary the width of a

microstrip and send a voltage pulse wave down it to measure

its operation as a function of width.

B. Theory

Figure 1 shows the geometry of a microstrip. As the

width to height ratio increases, more of the electric flux lines

are contained in the dielectric between the two conductors.

This causes the velocity to decrease since

V = c/sqrt(εr) (6)

And the dielectric constant εr is greater in the dielectric than in

air. The capacitance also increases when this happens, and

since Z0 = sqrt(L/C), Z0 of the microstrip is expected to

increase. The other parameters are then expected to change as

a result of this as found by examining equations (1) – (5).

Figure 1 – Geometry of a microstrip [1]

II. PROCEDURE

1) Cut out 6 microstrips out of tinfoil of widths 3, 6, 9, 12,

and 24 mm, each of length about 5 cm. After cutting them out,

measure these dimensions and write them down.

2) Tape these to a given dielectric supplied by the lab

instructor.

3) Use the TDR to measure and obtain the values V+, V

-, and

TD.

4) Use Equations (1) – (5) to calculate the rest of the desired

values using these measurements.

5) Plot Z0, v, λ/λ0, and εreff vs. width w.

III. CONCLUSION (RESULTS)

Table 1 summarizes the results and Figures 2 through

5 show the plots of Z0, v, λ/λ0, and εreff vs. width w. The height

h of the dielectric was measured to be 1.5 mm.

Table 1 – TDR Measurements and subsequent calculations

Figure 2 – Z0 vs. w

Figure 3 – v vs. w

Figure 4 - λ/λ0 vs. w

Figure 5 - εreff vs. w

It is apparent from Figure 2 that Z0 approaches a

constant value as the width of the microstrip gets larger in

comparison to the height of the dielectric h – a value about

equal to 24ohms. Judging from the Figures, in order for this

microstrip to have a characteristic impedance of 50 ohms, it

would have to have a width of about 2 to 2.5 mm, other

dimensions held constant. At this characteristic impedance,

the velocity of the wave through it would be about 1.25 *

10^8 m/s. The velocity did not get smaller as w/h increased as

expected. This may be due to extra reactances in the

microstrips of greater width due to wrinkles in the tinfoil.

Error may also be due to the interface between the

transmission line and the microstrip, which caused the

measurement of TD to be inaccurate.

As expected, εreff approaches a constant value as w/h

increases. As explained in [1], it approaches εr as w/h

approaches infinite, so using Figure 5, εr can be estimated to

be about 5.5. Compared to the given value of 4.5, this

constitutes an error of about 20%.

width, w (mm) 24 12 9 6 3

w/h 16 8 6 4 2

length (cm) 4.96 5.26 5 5.3 5.42

V+ (mv) 201.1 201.1 201.1 201.1 201.1

V- (mv) -73.7 -71.5 -54.72 -45.2 -14

Γ -0.366484 -0.35554 -0.2721 -0.22476 -0.06962

TD (nsec) 0.4105 0.459 0.4495 0.459 0.4395

Z0 (Ω) 23.180495 23.77109 28.60996 31.6484 43.4914

v (m/sec) 1.21E+08 1.15E+08 1.11E+08 1.15E+08 1.23E+08

λ/λ0 0.4027609 0.38199 0.370782 0.384895 0.411073

εreff 6.1646082 6.853247 7.273809 6.750192 5.917819

ACKNOWLEDGEMENT

Lab Partner – Yin Ling

REFERENCES

[1] M. O. Sadiku, Elements of Electromagnetics, New York:

Oxford University Press, 2010.

[2] C. L. Chen, "Notes on Transmission Lines," Sec. 10-11. (1986)