How do you connect a receiver or transmitter to an antenna? Simple - a transmission line. You are no
doubt familiar with transmission lines (sometimes abbreviated as tx lines).
If you plug any electric device into a wall outlet, the wires
that connect the wall outlet to the device is a transmission line.
However, transmission lines behave very oddly at high frequencies. In traditional (low-frequency) circuit theory,
wires connect devices, but have zero resistance. There is no phase delay across wires; and a short-circuited
line always yields zero resistance.
For high-frequency transmission lines, things behave quite differently. For instance, short-circuits
can actually have an infinite impedance; open-circuits can behave like short-circuited wires. The impedance
of some load (ZL=XL+jYL) can be transformed at the terminals of the transmission line to an impedance
much different than ZL. The goal
of this tutorial is to understand transmission lines and the reasons for their odd effects.
Let's start by examining a diagram. A sinusoidal voltage source with associated impedance ZS is
attached to a load ZA (which could be an antenna or some other device - in the circuit diagram
we simply view it as an impedance called a load). The load and the source are connected
via a transmission line of length L:
In traditional low-frequency circuit analysis, the transmission line would not matter. As a result,
the current that flows in the circuit would simply be:
However, in the high frequency case, the length L of the transmission line can significantly affect
the results. To determine the current that flows in the circuit, we would need to know what the input impedance
is, Zin, viewed from the terminals of the transmission line:
The resultant current that flows will simply be:
Since antennas are high-frequency devices (in the sense that their size is on the order of a half wavlength or more),
transmission line effects are often VERY important. That is,
if the length L of the transmission line significantly alters Zin, then the current into the antenna
from the source will be very small. Consequently, we will not be delivering power properly to the antenna. The
same problems hold true in the receiving mode: a transmission line can skew impedance of the receiver sufficiently
that almost no power is transferred from the antenna.
Hence, a thorough understanding of antenna theory requires an understanding of transmission lines. A great antenna
can be hooked up to a great receiver, but if it is done with a length of transmission line at high frequencies, the
system will not work properly.
Examples of common transmission lines include the coaxial cable, the microstrip line which commonly feeds
patch/microstrip antennas, and the two wire line:
When are transmission line effects significant?
We know that at low frequencies, transmission lines don't affect power transfer in practical applications
we use every day. However, at high frequencies, even short lengths of transmission lines will affect the
power transfer. Why is there this difference?
The answer is fundamentally important:
It is not the length of the transmission line, or what frequency we operate
at that determines if a transmission line will affect a circuit. What matters is how long the transmission line is,
measured in wavelengths at the frequency of interest.
If a transmission line has a length greater than about 10% of a wavelength, then the line length will noticably
affect the circuit's impedance.
Let's look at some examples to make this clear:
Let's say you plug your vaccuum cleaner into a wall outlet. The chord (transmission line) that connects the power
to the motor is 10 meters long. The power is supplied at 60 Hz. Should transmission line effects be taken into account?:
Answer: The wavelength at 60 Hz is 5000 km (5 million meters).
Hence, the transmission line in this case is 10/5,000,000 = 0.000002 wavelengths (2*10^-6 wavlengths)
long. As a result, the transmission line is very short relative to a wavelength, and therefore will not have much
impact on the device.
Example #2. Suppose a wireless device is transmitting at 4 GHz. Suppose also that a receiver is connect
to a microstrip antenna
via a microstrip transmission line that is 2.5 centimeters (cm) long. Should
transmission line effects be taken into account?
Answer: The wavelength at 4 GHz (4*10^9 Hz) is 7.5 cm. The transmission line is 2.5 cm long. Hence,
the transmission line is 0.33 wavelengths long. Since this is a significant fraction of a wavelength (33%),
the length of the line must be taken into account in analyzing the reciever/transmission line/antenna system.
Hopefully we now understand when a transmission line will affect the circuit. If you don't, read the last
two examples again until you understand. What we don't understand yet, is how the transmission line
messes things up. This will be covered in the next sections.
Next: Transmission Line Models and Z0
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