3 Layout Planning and Design
4.5 Design Rules for PCBs for Microwave Circuits
4.5.1 Basic Definitions
It was explained in the previous sections that in the case of high frequency circuits, the conductors on the PCB behave as transmission lines. Besides the characteristic impedance of the transmission line, there are some other useful terminologies which should be understood. These are listed below.
Fig. 4.19 Surface microstrip trace structure
Design Considerations for Special Circuits 175
Reflection Coefficient
When a power source is connected to a transmission line which is not terminated by its characteristic impedance, the energy gets reflected from the termination. The reflection is usually given as a fraction of the incident wave as follows:
r = Reflection coefficient = R flected wave amplitude Incident wave amplitude
e
Voltage Standing Wave Ratio (VSWR)
When a sinusoidal voltage is applied to a transmission line, the voltage at any point along it can be obtained by adding the incident and reflected voltages. In such a case, if the length of the line is greater than half the wavelength corresponding to the input frequency, voltage maxima and minima are established along the line. This is shown in Figure 4.20. From this, the voltage standing wave ratio (VSWR) is defined as:
V
V
V
V
l 2
l 2 Source point
t = t1
t = t1+
t = t1+
Voltages along the line at different times:
Superimposed results in a maxima/minima pattern.
T 4
T 2 x
x
x
x
Incident voltage Reflected voltage Resultant voltage f = Frequency, f = T = Period of signal t = Time
V = Voltage
x = Distance along the transmission line
= Wavelength l
1 T
Fig. 4.20 Voltage maxima and minima along a transmission line (redrawn after Bosshart, 1983)
VSWR= Maximum value of the voltage along the line Minimum value of the voltage along the line VSWR is related to r by the relation
VSWR = (1 + r )/( 1 – r )
Modes of Propagation
When a power source is connected to a transmission line, the wave propagation along the line can be described completely by describing the direction with respect to the propagation direction, magnitude and time variation of electric (E) and magnetic (H) waves. These two waves may have many possible orientations with respect to the propagation direction. Each possible orientation is referred to as a mode of propagation.
One of the most common types of propagation is the Transverse Electric and Magnetic (TEM) mode. In this mode, the electric and magnetic fields are perpendicular to the direction of wave propagation.
4.5.2 Strip Line and Microstrip Line
Today’s high performance PCB traces are manufactured as transmission lines. In principle, several types of planar transmission lines can be fabricated. However, the strip line and the microstrip line are the most common type and are therefore described below.
4.5.2.1 Strip Line
A strip line is basically a sandwich of two PCBs: one double-sided PCB with the transmission line on one side, and a ground plane on the other, and one single-sided PCB with ground plane over its entire area. This is illustrated in Figure 4.21. The mode of propagation is TEM. In this mode, the electric and magnetic fields are perpendicular to the direction of wave propagation.
w
t b
Dielectric constantser
b= Thickness of dielectric t = Thickness of centre conductor
(t =0for ideal strip line) w= Width of centre conductor Fig. 4.21 Practically realized strip line
Design Considerations for Special Circuits 177
There are typically two configurations of PCB stripline:
a Centred or Symmetric Strip Line: In this configuration, which is shown in Figure 4.22, the signal trace is sandwiched symmetrically, i.e. centred between the two reference planes.
This is often difficult to achieve as the laminate above and below the trace will be either C-Stage or B-Stage (core or pre-preg) material.
a Offset or Asymmetric Strip Line: In this configuration, shown in Figure 4.23, the trace is sandwiched between the two reference planes but is closer to one plane than the other.
T Center
line
W1 H
W
T
W1 H
W
H1
Fig. 4.22 Symmetrical strip line configuration Fig. 4.23 Offset or asymmetrical strip line
a Dual Strip Line: The structure of a dual stripline is shown in Figure 4.24, which has a second mirror trace positioned at distance H1 from the top ground plane. In this case, the two signal conductors are sandwiched between the two reference planes on adjacent layers.
These two signal layers will be routed orthogonally to minimize inter-layer cross-talk; i.e.
the signal layers are made to cross at right angles so as to minimize the crossing area. The structure then behaves as two independent offset striplines. (Polar Instruments, 2003)
T T Signal lines Ground/Vcc
reference plane H H2
H1
H1
A B
Fig. 4.24 Dual strip line
The value of the impedance of the stripline will be determined by its physical construction and electrical characteristic of the dielectric material. These factors are the width and thickness of the signal trace, the dielectric constant and height of the core or pre-preg material on either side of the trace and the configuration of trace and planes.
4.5.2.2 Microstrip Line
A microstrip line is nothing but a double-sided PCB with a conductor line on one side and a ground plane on the other side. This is illustrated in Figure 4.25. In other words, a microstrip transmission line consists of a conductive trace of controlled width on a low loss dielectric mounted on a conducting ground plane. The dielectric is usually made of glass-reinforced epoxy such as G10 or FR-4, or PTFE for very high frequency.
Dielectric,er
t = Thickness of centre conductor t
w
b
Ground plane
Fig. 4.25 Microstrip line construction
The mode of wave propagation in a microstrip line is not strictly TEM, but quasi-TEM. This is because of the discontinuity in the dielectric and the absence of symmetry of the ground plane with respect to the line conductor.
The important dimensions for the microstrip line are W (the upper track width), H (the laminate thickness) and G (the width of the ground plane). Ideally G should be infinite, but in practice, 10 W can be acceptable. For very low impedances, i.e. less than 30 ohms, it can be even reduced to 5 W.
Although straight lines are preferable when making a microstrip line, it is often necessary to use bends. For frequencies upto several GHz, low VSWRs are achieved if significant bends are trimmed at 45° as shown in Figure 4.26. Coaxial connectors to the boards are best inserted through the ground plane rather than at the board edges, as illustrated in Figure 4.27.
Connector
Ground plane Board
Fig. 4.26 For maintaining good VSWR, the stripline Fig. 4.27 Use of coaxial connectors inserted through
is trimmed at 45° corner the ground plane on a PCB
Design Considerations for Special Circuits 179
The following are the various configurations of a PCB microstrip (Polar Instruments, 2003b):
a Surface Microstrip: This is the simplest configuration and is shown in Figure 4.28. It consists of a signal line, with the top and the sides exposed to air, on the surface of a board of dielectric constant Er and reference to a power or ground plane. Surface microstrip can be implemented by etching one surface of double-sided PCB material.
a Embedded Microstrip: Also known as buried microstrip it is similar to the surface microstrip. However, the signal line is embedded (Figure 4.29) in a dielectric and located at a known distance H1 from the reference.
H Er
W
W1
T T
W1 H
W
H1
Embedded Microstrip
Fig. 4.28 Surface microstrip structure Fig. 4.29 Embedded microstrip with edge-coupled differential traces
a Coated Microstrip: This (Figure 4.30) is similar to the surface version. However, the signal line is covered by a solder mask. The solder mask coating can lower the impedance by up to a few ohms depending on the type and thickness of the solder mask.
a The equations for characteristic impedance for the microstrip require complex mathematics, usually using field solving methods including boundary element analysis.
4.5.3 Transmission Lines as Passive Components
Many electronic circuits such as tuned amplifiers, filters, etc., operating at microwave frequencies, make use of passive components like inductors and capacitors. However, their values are too small to be constructed by conventional means such as wound inductance and parallel plate capacitors.
Not only is the physical size too small but the parasitic effects may disturb the circuit function. In such situations, the only method is to use transmission lines of suitable length with suitable termination
T
W1 H
W
H1
Coated Microstrip
Fig. 4.30 Coated microstrip
as inductors and capacitors. Figure 4.31 shows a typical configuration of a transmission line connecting a source to a load.
By choosing a proper length of the transmission line, either an inductance or a capacitor of desired value at any frequency can be realized. It may be noted that
for a given length of transmission line, the value of inductance or capacitance is a function of frequency. Therefore, microwave circuitry can be realized on a PCB by having transmission line elements with suitable length and
termination. With developments in PCB technology and the availability of microwave dielectric materials, it is now possible to fabricate transmission lines in a single plane, wherein for all practical purposes, the width of the conductor controls the property of the transmission line. This has facilitated the formation of complex microwave circuits by interconnecting components to the transmission line elements.
As explained earlier, the transmission lines can be used as passive elements.
A line which is short in length as compared to the wavelength of the signal transmitted can be approximated as a lumped passive element such as an inductor or an individual capacitor. A thin line gives an inductance and a thick line, a capacitance. Of the various possible geometries, the flat spiral type is the most common because it provides the greatest inductance per unit area. With a double-sided board, the inductance per unit area can be increased by placing turns on both sides of the boards. Figure 4.32 gives the inductance values and shape for a range of printed flat spiral inductors. Where a simple low Q
Near end Far end
Source
t
ZL Load
Fig. 4.31 Transmission line connecting a source to a load
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.01 1.0
0.1 10.0
ID ID
track
width =0.5mm Spacing =0.5mm inner dimension
= ID 7mm
5mm 3mm ID =
´
´
´
´
´
´
´
´
´
´
´
InductanceL(H)m
Number of turns
Fig. 4.32 Inductance values and shape of printed flat spiral inductors transmission line connecting a source to a load (redrawn after Haskard, 1998)
Design Considerations for Special Circuits 181
inductor is required, the form as shown in Figure 4.33 can be used. Its inductance value for a given area is nearly one-tenth that of a spiral inductor.
These components can be used to make filters,
impedance transformers, matching devices, etc., for example, Figure 4.34 shows a low pass filter, which can be built using transmission line segments such as an inductor and capacitor. This circuit can yield low pass filter with a cut-off frequency in the range of a few megahertz.
C1 C2 C3 C4
L1 L2 L3
C1 C2 C3 C4
L1 L2 L3
Fig. 4.34 Low pass filter circuit and its microstrip form of realization
Transformers can also be realized in printed circuit form. Figure 4.35 shows several configurations used for making transformers. It may be noted that coupling on the meander transformer is low, typically fewer than 10 per cent whereas it can approach 90 per cent with spiral inductors.
Side 2
Board Side 1
(a) (b) (c)
Fig. 4.35 Examples of printed circuit transformers: (a) meander transformer (b) spiral transformer on one side of a board, and (c) using two sides of a board (after Haskard, 1998)
4.5.4 General Design Considerations for Microwave Circuits
The requirement of high accuracy for line width for microwave applications is much higher; otherwise it seriously affects the VSWR (voltage standing wave ratio). For example, consider a 75W source connected to a 75W load through a line whose characteristic impedance is exactly 75W. In such a case, no reflection takes place and the VSWR is exactly one.
Consider now a line whose characteristic impedance is 80 W, caused due to reduced line width and connected to the same load and source. Then the reflection coefficient r = (80 – 75) / (80 + 75) = 0.032
Fig. 4.33 Example of printed circuit meander inductor
and therefore VSWR is = (1 + r) / (1 – r )= 1.032 / 0.968 = 1.066. This shows that VSWR becomes poorer if the line width is not exactly what has been calculated.
To obtain high accuracy of line width, the artwork, should therefore, be made 4 to 16 times larger than the actual size while designing microwave PCBs.
The wave which propagates along the strip and microstrip transmission line gets attenuated due to: (i) dielectric loss (ii) loss in the conductor of the line, and (iii) radiation loss (mainly in the microstrip line). Therefore, PCB materials for microwave applications should be selected so as to yield minimum loss. This is achieved by choosing a material with high dielectric constant which reduces radiation and dielectric loss and results in reduction of the size of the microwave circuit, thus extending the usefulness of microwave PCBs to higher frequencies. The dielectric materials used at high frequencies, including microwave frequencies are Rexolite 1422 polystyrene, Silicon resin with ceramic powder filling and Teflon fibre-glass.