Let's say I have a 5 stage L-C ladder network with L= 4.7 micro Henry and C= 60 pF. The characteristic impedance of the network becomes 280 ohms (square root(L/C)). However, from circuit analysis, the impedance of the circuit becomes j*561 ohms at 25 MHz. If I want to drive a load of about 50 ohms which will be placed at the end of the L-C ladder network what impedance of the ladder network will come into consideration for matching? Will it be 280 ohms or j*561 ohms for maximum power transfer? The source is a 50 ohm AC source. I want to pass a signal of about 9 MHz through this ladder network.

Thanks in advance.

Sample schematic

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    \$\begingroup\$ Rather what will this undefined filter do, which can be easily bode plotted in Falsad’s site , what do you need? Define s11,s22,s21 \$\endgroup\$ Oct 24 '18 at 19:01
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    \$\begingroup\$ why use a mismatched filter? \$\endgroup\$
    – Neil_UK
    Oct 24 '18 at 19:07
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    \$\begingroup\$ The whole LC-chain-as-transmission-line approximation only works below the cutoff frequency. Around and above the cutoff frequency it looks like a low-pass filter. 1/(2*pi*sqrt(L*C)) is around 9.5MHz -- so it's really no astonishment at all that the thing looks purely reactive to the generator. \$\endgroup\$
    – TimWescott
    Oct 24 '18 at 19:13
  • \$\begingroup\$ Thanks for the comments. Actually, I am interested to know what will happen below 9.5 MHz for the mentioned value of inductor and capacitors. If it is a single L-C low pass filter I can understand it will attenuate high-frequency components over 9.5 MHz. However, I am not clear about how the chain L-C network will work below 9.5 MHz in this case. If I need to pass a signal from generator with a frequency below 9.5 MHz to a 50-ohm antenna what parameters should I consider to modify? I need to keep the L-C ladder network which is a constraint for me while ensuring signal transfer to load/antenna \$\endgroup\$
    – Allison_81
    Oct 24 '18 at 20:15
  • \$\begingroup\$ @TimWescott you are forgetting a transmission also needs a distributed R, so it has large ripples in the decade below cutoff. \$\endgroup\$ Oct 25 '18 at 10:10

Since each LC is loaded by smaller reactive load, each pole shifts after each successive “step” in the LC ladder. This results in a 6dB swing in the transfer function or +/-3dB from pole to pole till you get to the output.

I chose Falstad’s filter simulator since LC Ladder is a defined circuit, then stretched the y axis spectrum slider right THEN the frequency response so that I got near your values.

You can see the results here.

What you really want is a smooth low Q, flat group delay, Bessel flat response or a steep Chebychev maximally flat response. These 2 types which can be adjusted with more specs like 3dB flat or 6dB flat and degree of flatness unlike the LC ladder which has large de-tuned ripples. Chebychev staggers the peaks too but in a way that the ripple is minimized to any amount like 1dB or 0.1dB which trades off steepness of the skirt. There are many more options like Cauer Elliptical, raised cosine, Gaussian linear phase, etc.


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