Ian White, G3SEK wrote:
>
> bob alexander wrote:
> >The "exact" method isn't.
> Bob, you may be referring to the "old" ARRL method, which has all the
> faults you describe.
>
> This was superseded by a much more exact method, which after some years
> appeared in the 1995 Handbook and all editions since then.
>
> The new method is the one we're talking about here. It uses the concept
> of "input Q" and "output Q", but these are not the same as the overall
> network Q. When you analyse the complete network, the overall network Q
> is correct.
>
> 73 from Ian G3SEK Editor, 'The VHF/UHF DX Book'
> 'In Practice' columnist for RadCom (RSGB)
> http://www.ifwtech.demon.co.uk/g3sek
----------
Hi Ian,
I just pulled my 1998 ARRL Handbook off the shelf and opened it for
perhaps the first time this year. I had never read the section on
Pi-networks and the new "exact" method. I have never considered the
negligible Q of the output l-network part of a pinetwork to be of any
great significance. It is the Q of the input l-network that establishes
the bandwidth and harmonic rejection of the filter. For this reason, I
have always considered the design Q of a pinet to be that of the input l
network and never worried about what the output Q had to be.
I have always designed pi networks as back to back L networks.
Looking at the equations for this "exact" method, I have no problem with
the equation for Q1, or how Q2 is determined or with the equations for
Xc1 and Xc2.
There is, however, a problem with the equation for XL. It yields a
value of XL that results in insufficient inductance in the network.
That is why you end up with a higher resonant frequency than you
designed for when you do the math using the values derived from this
"exact" method. Your circuit for 7 MHz, Q=10, Rl=2000 and Ra=50 is a
good example. The values calculate to a resonant freq of 7.36 MHz not
7.00 MHz.
The solution is rather simple. Delete the equation for XL...
XL = (RL*Qo)/(Q1^2 +1)... and replace it with
XL = Xc1 + Xc2 (absolute values).
Again, using your example... recalculate XL using the above equation and
you get an inductance of 6.1729 uH. Now, do the calcs for resonant
frequency and you get 7.00 MHz. The input L network transforms
RL = 2000 ohms to 24.55 ohms ( Q=8.97). The output L network transforms
24.55 ohms up to 50 ohms (Q=1.03). Total Q = 10.
Now it really is "exact".
73, Bob, W5AH
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