Please review the general sinusoidal wave concepts in Secs. 3.8-3.10 and 5.7-5.10 of
RWVD (SES Chapters 1 and 2). Note carefully RWVD Example 5.8 (SES Sec. 2.6). In this
demonstration you will learn how to use a ``50 ohm'' slotted line, crystal detector, and
standing wave ratio meter to obtain the wavelength
and voltage standing wave ratio S on a coaxial transmission line. In a later
demonstration you will use these techniques to measure and control impedances and reflection
coefficients on a microwave transmission system.
The apparatus used is shown below. The slotted line is a (rigid) continuation of the coaxial transmission lines ``a'' connected at each end. It has a thin slot in its outer conductor, cut along z. A probe rides within (but not touching) the slot to sample the transmission line voltage. The probe can be moved along z, and can also be moved into and out of the slot by means of a micrometer. The probe is connected to a crystal (diode) detector that converts the time-varying microwave voltage to dc. The dc voltage is measured using the standing wave ratio (SWR) meter.
Suppose a sinusoidal voltage wave
travels from the RF generator through the slotted line and is incident on a load (resistor,
capacitor etc.) at z = 0. Here is the amplitude (generally a complex number) of the
wave,
and
, where f (in Hz) is the frequency, and
(in meters) is the wavelength. In general, a reflected sinusoidal voltage wave
is excited at the load and travels back through the slotted line toward the generator. The two
waves interfere, such that the total voltage displays a series of maxima,
and minima,
with successive maximum and minimum values separated in z by a distance . The
voltage standing wave ratio S is defined as
The crystal (Schottky-barrier diode) detector can be moved along z and samples a small
fraction of the total slotted line voltage v(t). For powers below 10 W reaching the
detector, the detector is a ``square law'' device, meaning that the dc output voltage
at b
is proportional to the (time average of the) square of the slotted line voltage v(t)
where denotes an average over a period
. The SWR meter expects
this and is calibrated accordingly. The constant of proportionality C does not matter, since
only voltage ratios are measured. It is common in microwave measurements to give the voltage
standing wave ratio in decibels (dB):
Set the RF signal generator to a frequency f = 750 MHz, 100% modulation at 1000 Hz, and 10 dBm (decibels above one milliwatt) output power. Connect the short circuit to the termination point.