Page 425 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

TESTING OF A MEMS-IDT ACCELEROMETER 405

method. Four standard methods are used, namely, shielded open circuit, short circuit, load,
and through. This method provides full correction for directivity, source match, reflec-
tion and transmission signal path frequency response, load match, and isolation for S 11,
S 12, S 21, and S 22. The procedure involves taking reflection, transmission, and isolation
measurements.
For the reflection measurements (S 11 , S 22), the open, short, and load standards are
connected to each port in turn and the frequency response is measured. These six measure-
ments result in the calculation of the reflection error coefficients for both the ports. For the
transmission measurements, the two ports are connected and the following measurements
are conducted: forward transmission through (S 21 -frequency response), forward match
through (S 21-load), reverse transmission through (S 12-frequency response) and reverse
match through (S 12-load). The transmission error coefficients are computed from these
four measurements. Loads were connected to the two ports and S 21 noise floor and S 12
noise floor levels were measured. From these measurements, the forward and reverse
isolation error coefficients are computed. The calibration is saved in the memory of the
network analyser and the correction function is turned on to correct systematic errors that
may occur.

14.4.3 Time Domain Measurement

The relationship between the frequency domain response and the time domain response
is given by the Fourier transform, and the response may be completely specified in
either domain. The network analyser performs measurements in the frequency domain
and then computes the inverse Fourier transform to give the time domain response. This
computation technique benefits from the wide dynamic range and the error correction of
the frequency domain data.
In the time domain, the horizontal axis represents the propagation delay through the
device. In transmission measurements, the plot displayed is the actual one-way travel time
of the impulse, whereas for reflection measurements the horizontal axis shows the two-way
travel time of the impulse. The acoustic propagation length is obtained by multiplying the
time by the speed of the acoustic wave in the medium. The peak value of the time domain
response represents an average reflection or transmission over the frequency range.
The time band pass mode of the network analyser is used for time domain analysis. It
allows any frequency domain response to be transformed to the time domain. The Hewlett
Packard (HP) 8510B network analyser has a time domain feature called windowing, which
is designed to enhance time domain measurements. Because of the limited bandwidth
of the measurement system, the transformation to the time domain is represented by a
sin(x)/x stimulus rather than the ideal stimulus. For time band pass measurements, the
frequency domain response has two cutoff points f start and f stop. Therefore, in the time
band pass mode, the windowing function rolls off both the lower end and the higher
end of the frequency domain response. The minimum window option should be used to
minimise the filtering applied to the frequency domain data.
Because the measurements in the frequency domain are not continuous but, apart from
Af (in Hz), are taken at discrete frequency points, each time domain response is repeated
every 1/Af seconds. The amount of time defines the range of the measurement. Time
domain response resolution is defined as the ability to resolve two close responses. The