Electrical – Matching impedance network for an LC ladder network


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

Best Answer

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.