# Rlc tuning

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#### jcm2009

##### New Member
Hi, I'm building a radio frequency coil (for use in MRI). Each coil is an RLC circuit, but the size and shape are predetermined (both R and L are a function of this) and so all I can do to tune the coil to resonate at the right frequency (127.74 MHz) is change the capacitance. Ideally the circuit will have an impedence of 50 ohms and a phase difference of 0 at this frequency, and I have successfully achieved these values with the right capacitors.

The problem I face is when placing different 'loads' inside the coils (different types of tissue, etc). 'Loading' the circuit shifts the resonant frequency by a little bit. However this is a problem because my impedence peak is very narrow. So I can have Z at nearly 50 and the phase at almost 0 at 127.74 MHz, but then even a slight change in the resonance frequency causes tremendous changes in both impedance and phase values at the 127.74 MHz point because the peaks are so steep (changes as high as 30 ohms or degrees respectively at that frequency)

My question then is how can I get a broader impedence peak so that even if the frequency changes a bit this will not lead to large changes in phase and impedence? I don't know if I'm being clear enough with my question so if you need more information please let me know.

Thanks a lot I have to assume that the total resistance (R) including the coil resistance is 50 ohms and that your RLC circuit is a series RLC circuit, since all you had to do to obtain both 50 ohm impedance AND 127.74 MHz resonant frequency simultaneously was to tweak the capacitor.

Given that, you broaden the response by inserting a series resistor (Rs) into the your series RLC circuit. The impedance at resonance will be 50 ohms plus Rs. You then add another resistor (Rp) across that circuit to obtain 50 ohms impedance for the total circuit at resonance, such that Rs + 50 in parallel with Rp equals 50 ohms.

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