Impdedance matching for complex output

Hi, I have questioned regarding the impedance matching for this circuit and dont know how to solve this problem. Circuit is below:



I would like to separate or match 500 ohms source with the complex (roughly 1 ohms) in the right for many frequency in bandwidth 100KHz and centre fo at about 42KHz. SO how to do with this matching circuit. I have searched that we can use L, T or pi type with matching. But all of them do with one frequency. Thanks

A (simple) matching circuit is usually working at one frequency.
With more complex matching circuits you can achieve a "broadband" machting, hints are for example is these pdf: https://www.rfmd.com/cs/documents/hfe0109_bichler.pdf
You can calculate different matching circuits on this web page: https://home.sandiego.edu/~ekim/e194rfs01/jwmatcher/matcher2.html

How would it be 100kHz Bandwidth at 42kHz center frequency ??? Is it 42MHz ???

Didn't notice it either but matching for negative frequency values, interesting problem. A possible problem in a weird mixer situation maybe.

Assume 42 MHz, assume Murata LQG18H inductors.
It is critical to include component losses in a such extreme impedance ratio so if other types of inductors are preferred must network be recalculated.
Capacitors are assumed to be of good quality.





A simpler L network will result in a slightly more narrow impedance but component values will be more critical.
A comparison, with curves above in red:

Hi flanello, Bigboss and E Kafeman, It is 42 KHz (from LC) not 42 MHz. Assuming tunning C so frequency will change within 100KHz. I think impedance by L, C , pi type will not work for this situation since it changes 42KHz also. I think about the op amp which could separate 500 ohms and 1 ohms but could not find any. Do you know any opamp that could separate this 500hms (real resistance) and the complex impedance on the right? I have tried with opa380 and LM318 but is failed. ANy recommendation circuit please. Thank you very much !

42 kHz is obviously not center frequency if frequency range is 100 kHz wide, Actual frequency range is unknown and maybe is load impedance something that dynamically is changed within this frequency range, as a part of setting frequency of interest. Maybe is bandwidth of interest just the resonant frequency in a certain tunable range.
I'll try to answer according to this.
If you still want to design a matching circuit and you are tuning load with a variable C, then must also matching circuit be tuned correspondingly to the new impedance situation.
A matching circuit can not be designed for more then one fixed situation if designed with fixed components.
The matching circuit internal structure is not relevant as long as it fulfills to be the complex impedance conjugate.
In much does, how I understand your problem, reminds me of how an old superheterodyne radio is designed with a local oscillator and several tuned filters, all controlled by a multi section tunable capacitor.
Looking at a such circuit can maybe give some ideas related to your circuit.

An new alternative seems to be implementing an op-amp without intention to improve impedance matching. Guess you says that wide band impedance matching not really is of interest.
You want a circuit that can feed internal losses in a resonant circuit, without burning the op, at resonance frequency where load is a pure resistive impedance.
Small-signal op-amps have relative high internal serial resistance for the output stage, typical 20-100 Ohm.
If you want to match a such circuit to deliver power in 1 Ohm resistive load more effective can it be done with a regular winded impedance transformer in between. A such transformer can be relative wide band in its behavior.
Adding a PA stage with some low impedance transistors is another possibility.