Designing Practical LC Resonant Circuit Using an Online Calculator

Here, we will design a parallel LC resonant circuit using an example that requires us to provide a 3-dB bandwidth of 10 MHz at a center frequency of 100 MHz. We will use an online LC resonance circuit calculator to calculate the necessary values of inductance (L), capacitance (C), and parallel resistance (Rp). I’ll also walk you through the steps to simulate the circuit and demonstrate that it indeed works at the specified frequency.

Problem Statement:
We are tasked with designing a simple parallel resonant circuit that satisfies the following conditions:

Center frequency (f₀): 100 MHz
3-dB bandwidth: 10 MHz
Source and load impedances: 1000 ohms each
Capacitor assumption: Lossless
Quality factor (Q) of inductor: 85

Our goal is to use the LC resonant circuit calculator to determine the values of L, C, and Rp, then verify the design through simulation.

Step 1: Understanding the Design Formula
For a parallel resonant circuit, the relationship between the quality factor (Q), bandwidth (BW), and resonant frequency (f₀) is given by:

$Q = \frac{f_{0}}{B W}$

From the equation for quality factor, we know:

\begin{matrix} Q = \frac{R_{t}}{X_{p}} & (1) \end{matrix}

which can be rearranged as:

X_{p} = \frac{R_{t}}{Q}

Once we know $X_{p}$ , we can calculate the inductance (L) and capacitance (C). However, to find $X_{p}$ , we first need to know the total resistance $R_{t}$ , which is the parallel combination of all resistances in the circuit. The total resistance $R_{t}$ is given by:

\begin{matrix} R_{t} = R_{p} ∥ R_{s} ∥ R_{l} & (2) \end{matrix}

where $R_{s} = R_{l} = 1 k Ω$ (as given).

The quality factor $Q_{p}$ for the inductor is:

Q_{p} = \frac{R_{p}}{X_{p}}

or equivalently,

\begin{matrix} R_{p} = Q_{p} \cdot X_{p} & (3) \end{matrix}

Substituting equations (1) and (2) into this expression, we get:

X_{p} = \frac{(R_{p} ∥ R_{s} ∥ R_{l})}{Q}

Using equation (3):

X_{p} = \frac{(Q_{p} \cdot X_{p}) ∥ R_{s} ∥ R_{l}}{Q}

Simplifying further, we obtain:

\begin{matrix} X_{p} = \frac{R_{s} \cdot R_{l}}{R_{s} + R_{l}} \cdot (\frac{Q_{p}}{Q} - 1) & (4) \end{matrix}

Now, with $X_{p}$ known, we can calculate the inductance (L) and capacitance (C) as follows:

L = \frac{X_{p}}{ω}

and

C = \frac{1}{ω X_{p}}

where $ω$ is the angular frequency, given by $ω = 2 π f_{0}$ .

Step 2: Using the LC Resonant Circuit Calculator
We can now use the LC resonance circuit calculator to quickly compute the values of inductance (L), capacitance (C), and parallel resistance (Rp). Entering the known parameters of center frequency (100 MHz), bandwidth (10 MHz), and source/load impedance (1000 ohms) will provide us with the exact component values.

Step 3: Simulation
After obtaining the L, C, and Rp values, it’s essential to simulate the circuit to verify that the design performs correctly at the specified frequency.

LC resonant circuit frequency response graph

The following video shows how to use the calculator, input the calculated values into a simulation tool, and verify that the circuit resonates at the intended 100 MHz frequency.

Conclusion:
Designing an LC resonant circuit can be made simple with the help of an online calculator. By following the steps outlined in this post, you can calculate the values of L, C, and Rp and verify the functionality of the circuit through simulation.

Related Resources:
For more in-depth information on related topics, you can check out the following posts:

Learn how to use impedance matching techniques with a Tapped-C Impedance Transformer Matching.
If you are designing your own inductors, take advantage of this Straight Wire Inductor Calculator.
Explore how to design power amplifiers with this Class Power Amplifier Calculator.

Designing Practical LC Resonant Circuit Using an Online Calculator

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