Lab 6 – Transmission lines and signal propagation
In this laboration you will study reflections in a system, their cause and how to terminate
them.
At low frequencies (or short lines) a line is just a short circuit. We don't have to consider
its length or other characteristics. As frequencies increase, we must consider the delay of
the line. We can no longer just think of the signal as a stream of electrons, but must
model it as an electromagnetic pulse. A wave of finite length traveling along the
transmission line at a finite speed. The characteristics of the transmission line now
become crucial to the quality of the signal.
Basics of a transmission line.
The impedance for a transmission line is:
Z(w) = sqrt[(jwL+R)/(jwC+G)]
A transmission line is a distributed series of inductors and capacitors. As the signal
propagates through the line it charges the capacitors causing a return current (ground
plane on a circuit board, shield of a coaxial cable). The return current follows the path of
least impedance which for low frequencies, where the resistive component dominates the
impedance, is the path of least resistance. For high frequencies the inductive part of the
impedance dominates and the current takes the path of least inductance.
An ideal transmission line is simply a time delay. The input state is transported without
distortion to the output. In reality there are frequency dependent losses. At low
frequencies it acts as an RC component. At high frequencies the current is no longer
propagating in the entire conductor, only at the surface, which will cause the resistance to
increase and correspondingly the impedance increases (This is called skin effect). At
even higher frequencies the current loss through the dielectric material becomes a factor.
Ideally one should use a transmission line in the LC region. A frequency range where the
impedance is dominated by the ratio between inductance and capacitance, and the high
frequency dependent effects are small.
In a coaxial cable, the electromagnetic field is contained inside the shield. The impedance
is independent of the surrounding medium. What decides the impedance is the
dimensions of the cable and the dielectric material between conductor and shield.
Any impedance discontinuity gives rise to reflections. An ideal system has continuous
impedance, no reflections occur and the system is easy to predict and control. An
example of an ideal system is an infinite transmission line. In reality, the line ends and we
get reflections. To minimize these reflections we give the current a return path besides
reflecting back the line. Two common terminations are:
Parallel termination - a resistor connects the signal line to ground ( or power). If the
resistance is the same as the characteristic impedance of the transmission line (and
assuming a perfect ideal resistor, no capacitance or inductance), this is the same as an
infinite transmissions line. The signal will cancel out at the termination.
Series termination - a resistor is placed in series with the signal line in order to match the
source (or end-) impedance with the impedance of the transmission line.
Formula for reflections:
Vr = Vo[(Z-Zo)/(Z+Zo)]
Another important aspect is how the transmission line and terminations effect rise time,
amplitude and power consumption. Any current loop requires power. Changing the
resistance changes the power. Capacitors takes time to charge. Inductors resist current
change.
It is always important in which direction the signal is moving along the transmission line.