IEEE Circuits and Systems Magazine - Q3 2020 - 39

C. Parallel Lines and Crosstalk
Crosstalk can happen between two
adjacent lines, when a signal on one
line can cause adverse changes on
the other. This is due to the electromagnetic fields, and the current
distribution below a microstrip line,
which results in a crosstalk given
by [29]
	

Crosstalk =

K

2
1 +` d j
H

. (5)

Where K < 1 is a constant that depends on the length of the lines
and the rise time, d is the distance

Vpulse

τRISE

tP

τRISE

tP
(a)
tP
τRISE

tP

(b)

Figure 4. (a) When the rise time is >2 × tP, the line (PCB trace)
can be considered electrically small. (b) For long lines, with
respect to xRISE, matching should be considered.

-20
Vpulse (dB)

Vpulse

B. 90° Turns
The previous discussion of transmission lines assumes
a straight line. It is often required to turn a transmission
line to reach a pin or a connector for example. Typically,
turns are limited to 90°. Sharper turns are usually broken down to two less sharp turns.
In Fig. 8(a), a group of various turn types are shown,
along with their corresponding measured and simulated
transmission [Fig. 8(b)] and reflections [Fig. 8(c)] (the
measurement equipment are limited to 8.5 GHz). Square 90°
and rounded turns result in high reflections and insertion
loss. As a result, they are not recommended especially
for high frequencies. Mitered lines are common and are
usually embedded in CAD tools and have a reasonably
good performance in the low GHz regime. Curved lines,
and double-45° lines, cause much less variations in the microstrip. As a result, they provide
the best performance compared to
a straight line.
The discrepancies between the
simulated and measured results
in Fig. 8 are primarily due to calibration setup limitations, in addition to fabrication tolerances. The
Time
trend of the turn type versus losses, however, remains consistent.

between the lines, and H is the height of the substrate.
From (5), it can be concluded that, in order to reduce
crosstalk, the distance d should be increased with respect to the substrate height, rather than the wavelength. Other techniques include adding resonators
between lines [6], which behave as a Bandstop Filter
(BSF), reducing coupling. Also, orthogonal routing on

-40

-20

dB

/De

cad

e

-60
-80
107

108
109
Frequency (GHz)

1010

(a)

Vpulse (dB)

one layer to another, return path vias are added. The
ground is also cleared between the differential vias to
maintain the coupling between the lines, as illustrated
in Fig. 7(b).
To transition a microstrip to a CPW (for probing for
example), many structures exist. This transition is the
topic of many published work [26]-[28]. As a result, the
choice is dependent on the -operating frequency and test
equipment. Design dimensions are typically optimized
using FEM simulations.

ftransition ≈ 0.22/τRISE ≈ 73 MHZ
-20 -2
0d
B/D
eca
-40
-4
de
0d
B/D
-60
ec
ad
e
-80

-100
Time

107

108
109
Frequency (GHz)

1010

(b)
Figure 5. (a) A digital signal, with a theoretical zero rise time, has a −20 dB/decade
envelope in the frequency representation. This can result in significant high-frequency
components. (b) A finite rise time will add an additional −20 dB/decade to the response,
suppressing high-frequency components. The signals are at 10 MHz. The rise time in
(b) is 3 ns. Transition frequency is calculated by setting the first expression in (4) to
1/ 2 and solving it numerically.

THIRD QUARTER 2020 		

IEEE CIRCUITS AND SYSTEMS MAGAZINE	

39
IEEE Circuits and Systems Magazine - Q3 2020

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