El-Arwash, "An optimal design of single

tuned filter in distribution systems," Electric Power Systems Research, vol.

In the early work of varactor

tuned filter developments, the center frequency was tuned by loading the varactor diodes at the ends of resonating stubs [4].

where [[omega].sub.0] = 1/[square root of([L.sub.i][C.sub.i]) (i = 1,2,3) is the midband angular frequency of filter, FBW = [DELTA][omega]/[[omega].sub.0] is the fractional bandwidth, and [bar.Y] is the normalized admittance matrix, which in the case of synchronously

tuned filter is given by

ADI reduced the amplitude of the unwanted sideband into a load by designing a

tuned filter network to provide the proper sum termination as a function of the RF and LO frequencies.

Since the resistor value is infinity, the high pass filters it self will work as a series

tuned filter. The tolerance and aging of components can make the shunt passive filter detuning.

The coupling matrix [M] is allowed to have nonzero diagonal elements [M.sub.ii] for an asynchronously

tuned filter. The excitation vector is given by [e]t = [1, 0, 0, 0].

This method requires a skilled operator and a "golden" filter to compare time response between the

tuned filter and an ideal one.

For example, in the case of

tuned filter production, the first filter units should be tested initially using a VNA (with a measurement result traceable to National Institute of Standards and Practices standards).

Among different attitudes towards the microwave filter tuning the one that refers to the coupling matrix describing the filter is powered by the simple idea: generally speaking, we want to have the ideal coupling matrix [M.sub.0] of the correctly

tuned filter and, based on the measured reflection characteristics, the detuned coupling matrix M.

Frequency range (GHz) 2.5 to 4.0 Insertion loss (dB) 5.0 3 dB bandwidth (MHz) 30 to 60 Coarse selectivity (dB) 36 Tuning coil current (A) 0.5 Switch time ([[micro]second]) 15 Weight (g) 80 Characteristics of a

tuned filter compared to the [S.sub.21] characteristics of a YIG-tuned filter based on equal insertion passband losses are shown in Figure 7.

Let us assume that we have M points representing the filter characteristic denoted by s [member of] [R.sup.M] and, by [s.sub.0] [member of] [R.sup.M] , the characteristic of a properly

tuned filter. We shall denote the values of N tuning element positions of a filter by z [member of] [R.sup.N].

The YIG

tuned filter (YTF) is one of the more difficult devices to measure because of its sensitivity to current fluctuations in its tuning coil (in this case 10 rad/mA) and its sensitivity to temperature variation, as shown in Figure 9a.