ranlevi said:
Hi all,
I'm a newbie when it comes to filters. I've recived a schematic at work
which
has an LC Pi filter as part of a video circuit. How do I go about
analyzing that filter? How can i derive, from the given L & C values,
what's the filter transfer function and behavior?
Any input is welcome,
If you label the impedances like this:
z1, z2, z3 for the left leg, center, and right leg of the PI network,
and
z0, zL for the input and output impedances, respectively,
the formula for Vout / Vin will be
z1*z3*zL / (z0 *z3*zL + z1*z3*zL + z0*z1*z2*z3 + z0*z1*z2*zL +
z0*z1*z3*zL),
(reduced from a voltage divider expression by CAS).
Given the formula, plug in the values for z0 and zL (for example, 50
ohms, or whatever), then put in the values for z1, z2 and z3 in terms
of the variable s. For an inductor, use the inductance times s, so for
a 0.1H inductor, use just 0.1s. For a capacitor, plug in 1/(s*C), so
for a 1000 uF capacitor, it would be 1/(1e-3s) or 1000/s. That gives
you a transfer function, and if you use a CAS, it will simplify a lot.
For example, the formula above, for 50 ohm input and output impedance,
with z1=z3=0.1H, z2=1000uF, reduces to
0.5s^2 / (25.5s^2 + 750s + 2.5e5 ).
At this point you can plot it or evaluate it in the frequency domain by
substituting jw for s, where j = sqrt(-1) and w = radian frequency (or
2pi*f ). When you plot it, you should take the absolute value of the
result for the magnitude, or its angle if you want to plot phase. For
the values given above, the filter magnitude response shows a rise from
-infinity to a resonant peak at 100 rad/sec (15.91Hz), and then levels
off to + infinity at -34db.
If you have Matlab, you could put the above transfer function in by
myTF = tf ( [.5, 0, 0] , [25.5, 750, 2.5e5] ), just putting the
numerator and denominator in, in descending powers of s. At that point
you can use Matlab to plot frequency response or time domain response
quite easily: bode(myTF), step(myTF).
