Design Ideas: June 9, 1994
First choose R, L, and C such that
where R is the effective resistance and equal to
By choosing C1 and L1 such that
and
the third-order term in the expansion series of Eq 1 vanishes, leaving only the first-order (lin- ear) term and the fifth- and high-order terms such that
The time delay (t) between the input and the output is, therefore, expressed by the approximate formula
which has an error on the order of 1%, even at frequencies as high as F0/2. Of course, it's normal first to choose R, L, and C to get the required t and then calculate proper values for C1 and L1
Two more things worth noting about this circuit are a. The filter exhibits frequency-independent delay and gain, regardless of the load resistance (r). The load resistance affects the attenuation factor (k) as follows:
b. Input impedance is purely resistive and equal to
which facilitates cascading the filter. The following values produce a time delay of 50 nsec: R0=150V, L=3.3 mH, L1=1 mH, C=150 pF, C1=47 pF, r=3 kV, f0=7.2 MHz. As Fig 1 shows, you can connect the output of the filter to a differential amplifier with the gain of 1.05 (1/k) to compensate for the attenuation factor k. (DI #1441)
