From: Nick Kennedy (email@example.com)
Couldn't let it rest. The whole Y-parameter thing. I usually like to skip
over that complicated stuff in the data sheets, apply some tried and true
ham rules of thumb, and hope for the best. But now the question of whether
y11 can be transformed directly into the input Z has nagged at me.
Wes Hayward's Intro to RF Design discusses two port networks and all the
various ways of characterizing them: y's, pi's, z's and s's in chapter 5.
Strikes fear into a mathophobic's heart.
Basically you view the doohickey as a black box with two input terminals (
the "1" end) and two output terminals (the "2" end). In the case of y
(admittance) parameters, tests are done to come up with four y parameters
such that these equations are true:
(1) I1 = y11*V1 + y12*V2, and
(2) I2 = y21*V1 + y22*V2
Where I1 and V1 are the input current and voltage and I2 and V2 are the
same at the output.
We'd like to know the input admittance, which is the reciprocal of the
impedance and is equal to I1/V1. From equation (1), you can see that if it
weren't for that pesky second term, I1/V1 would simply equal y11, which is
given in the data sheet. But no--it seems that the output voltage is going
to have some effect on the input current, and therefore on the input Y.
Hayward gives the formula for calculating input admittance from the y
parameters and connected load admittance (YL) as follows:
(3) Yin = y11 - (y12*y21)/(YL + y22)
Now, onward to the MC1350 data sheet. Does it give all those parameters so
we can crank this thing out? Pretty much, but it's kinda coy about one or
two of them.
At 10.7 MHz,
y11 = 0.36E-3 + .5E-3j
y22 = 4.4E-6 + 110E-6j
y21 = 160 at an angle of -19 degrees (specified in polar, for some reason)
y12 = << 1.0E-6 (much less than 1 micromho, absolute value)
They give the y12 << 1E-6 a couple of times, like they're bragging. Wonder
why? Well, it's that pesky factor in equations (1) and (3) that complicate
life. If it were small enough to render those terms negligible, then the
input impedance would simply be y11 and life would be better. Is that what
they're telling us? The output doesn't affect the input to an appreciable
Crank it out on Excel. Using the complete equation and 5k ohms for the
load, I get Zin = 976 -1294i ohms. By converting just y11 to Z, I get 948
- 1317i ohms. Not a lot of difference. In this case at least, Z = 1/y11
is a good approximation.
You might match to this thing by using a series inductor to cancel the 1300
ohms capacitive and them match to the 976 ohms resistive. Another,
probably better, way is to convert these series form numbers into
equivalent parallel ones. A series form Z of 948 -1317i is the same as an
R of 2777 ohms in parallel with Xc of 1999 ohms. That Xc at 10.7 MHz is
equivalent to a parallel C of 7.3 pF. Since ladder filters typically have
a shunt C at the end, it's value could just be reduce by 7.3 pF and the
filter designed to match 2777 ohms.
End of raving. Closed course, inexperienced driver, no QA department, your
results may be significantly different.
And now it's almost time for Arkansas Vs. Alabama.
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