Design Series LCR Circuit for 88MHz, 99MHz Rejection - 8 Ohm Load

[Nick90]

Homework Statement

A radio reciever requires a tuning circuit that will select 88MHz but reject 99MHz, design a series LCR circuit that will filter this way for a 8 ohm load resistance. State any assumptions. The circuit should be in the following format

http://cnx.org/content/m21475/latest/pic012.png

with a variable frequancy were the voltage is, and the output either side of the resistor.

Homework Equations

Think I am meant to use f=1/2pi*root(LC)

The Attempt at a Solution

confused about why the equation doesn't have any values for resistance in, I've searched a lot and found no relevant equations to include R.

Any help would be greatly appreciated. :D

 

[mark726]

Thank you for your question. I am happy to assist you with designing a series LCR circuit that will filter the desired frequency range.

First, let's start with some assumptions. We will assume that the 8 ohm load resistance is purely resistive and does not have any inductive or capacitive components. We will also assume that the tuning circuit will be connected in series with the receiver.

Now, let's move on to the solution. As you correctly mentioned, the equation for the resonant frequency of a series LCR circuit is f=1/2pi*root(LC). However, in order to design the circuit to filter out 99MHz, we will need to calculate the values of L and C using the desired frequency of 88MHz.

Using the equation, we can rearrange it to solve for L, giving us L = (1/4pi^2*f^2*C). Plugging in the desired frequency of 88MHz and using a standard value of 1 microfarad for C, we can calculate the value of L to be 2.01 millihenries.

Next, we need to determine the value of the inductor and capacitor that will create a notch at 99MHz. To do this, we can use the equation for the resonant frequency of a parallel LC circuit, which is f=1/2pi*root(1/LC). Solving for C, we get C = (1/4pi^2*f^2*L). Plugging in the desired frequency of 99MHz and using the value of L calculated earlier, we get a value of 1.61 microfarads for C.

Now, we can construct the circuit as shown in the format given in the forum post. The variable frequency source will be connected to the series LCR circuit and the output will be measured on either side of the resistor. As the frequency is varied, the voltage output will be highest at 88MHz and significantly lower at 99MHz, effectively filtering out that frequency.

I hope this solution helps you in designing your circuit. If you have any further questions, please do not hesitate to ask.