# Which is better for resonant frequency in terms of capacitor and inductor?

Calculating a resonant frequency requires a capacitor and inductor.

I'm trying to figure out the optimal capacitor and inductor values for 49Mhz.

Is it recommended to go for a lower inductor value and higher capacitor value? or vice versa? I'm aiming for best quality.

For example, should I go for 22pF and 480nH inductor or should I go for a 12pF cap and 879nH inductor?

The inductors I will use are premade axial and the capacitors might be ceramic disc.

• Inductor size will affect bandwidth / Q. Bigger inductor gives you sharper Q. But with sharper Q, it will be more difficult to produce the desired frequency exactly. Capacitance varies especially if it's 12pF. Actually if it's that small, you might be able to add a trimmer capcaitor. Not sure about drift though. – squarewav Sep 13 '16 at 4:44
• Please clarify "quality". Did you means quality factor "Q" as in resonator Q? – glen_geek Sep 13 '16 at 4:54
• What is the application? Can you show us a circuit diagram? – Bruce Abbott Sep 13 '16 at 7:21

You have a choice of inductor and capacitor value, that's 2 unknowns. If you know the frequency you want, that fixes their product.

If you are doing a simple school question, job done. Choose the value of one of them arbitarily, and calculate the other.

If the resonant circuit is for a specific purpose however, then you may be able to use other constraints.

The sqrt(L/C) of the components is called the impedance. You may want to control the ratio between your resonant circuit impedance and other components surrounding it. Generally, most transistor/IC applications will end up with a few 10s of ohms to a few kohms impedance, though specialist applications like RF transistor matching or Tesla coils will use lower or higher values respectively.

Closely related is the Q. If you have resistive loading, then the ratio L/R at the resonant frequency will give you the Q. A high Q means a narrow bandwidth, and a very 'ringy' response. A low Q means a wide bandwidth, and a very damped response.

If there is no external resistive loading, and no other constraints, then maximising the Q of the L with respect to its own internal R would be most people's definition of optimal. Go to an inductor catalogue, and tabulate a few Ls and residual Rs, for any given family of inductors. Work out the corresponding C and Q for the target resonant frequency. Warning, the optimum changes with inductor family.

Until you want to control the Q, or the impedance, or the bandwidth of your resonant circuit, you must choose one arbitarily.

• What I want to do in the end is transmit digital data wirelessly. I at first tried transmitting on 350Mhz but when I heard about the existance of stray capacitances, I immediately switched my circuit to operate at between 22 and 88 Mhz. Also, I'm not picky on data speed. If I can get a speed of 500 bytes a second, that would be fantastic. I probably can even get away with 100 bytes a second. I figured the inductor value can control this since it affects Q which affects bandwidth. – user116345 Sep 13 '16 at 18:01
• At 20MHz, no practical LC values will give you a bandwidth so narrow that it limits your data rate below 10s of kbit/s, you'd need a crystal filter or superhet to do that. If you're asking these sort of questions about LC and bandwidth for 22, 88 or 350MHz carrier, you're not ready to build a radio link from scratch. Buy a pair of 433MHz digital modules, or if the range isn't that big, a pair of ultrasonic transducers. They tend to have a bandwidth around 1kHz, so 100 to 500bit/s should be just right. – Neil_UK Sep 13 '16 at 20:02
• 1st specify is Series (SRF) or parallel (PRF)
• 2nd specify series R or parallel load R
• 3rd specify desired gain at resonance up to Q=100 for practical purposes.

• Then compute impedance ratio = Q = gain

• For series Zc/R = Q

• For parallel R/Zc = Q
• At resonance Zc(f) = ZL(f)

For a really fast graphical lookup for values use this chart with one known value and compute all others. (Print and keep)

http://www.testecvw.com/carl/images/impedancenomograph.pdf

Design assumes the Q and SRF of each part is higher than end result