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Chapter 19: Problem 13

Using the software, implement an inverting band-pass filter with a center frequency of \(15 \mathrm{kliz}\), a gain of 1 , and a \(Q\) of 10. Using simulation, verify that the circuit is operating as expected.

Short Answer

Expert verified
Design an inverting band-pass filter with the given specifications using a combination of an inverting high-pass filter and an inverting low-pass filter. Calculate component values using the provided formulae and implement the circuit in a simulation software. Run a frequency response analysis and verify the filter's performance by checking the gain at the center frequency and the 3-dB bandwidth. Adjust the design if necessary until the desired filter characteristics are achieved.

Step by step solution

01

Understanding the filter specifications

We need to design an inverting band-pass filter with the following specifications: 1. Center frequency (\(f_c\)): \(15 \mathrm{kHz}\) 2. Gain (\(A\)): 1 3. Quality factor (\(Q\)): 10
02

Designing the filter circuit

To design an inverting band-pass filter, we can use a combination of an inverting high-pass filter and an inverting low-pass filter. With the given specifications, design a circuit using appropriate components (resistors, capacitors, and operational amplifiers). The values of the components can be calculated using the following formulae: For the high-pass filter: 1. \(f_c = \frac{1}{2\pi R_1 C_1}\) 2. \(A = -\frac{R_2}{R_1}\) For the low-pass filter: 1. \(f_c = \frac{1}{2\pi R_3 C_2}\) 2. \(A = -\frac{R_4}{R_3}\) Use these equations to calculate the component values and design the filter circuit.
03

Implementing the filter circuit in a simulation software

Choose an electronic simulation software (e.g., LTspice, Multisim, PSpice, etc.) and implement the designed filter circuit. Verify that the component values are correct in the schematic and ensure the connections are accurate.
04

Simulating the filter performance

Run a frequency response analysis on the designed filter circuit and plot the output in terms of gain (in dB) as a function of frequency. Verify that the circuit is operating as expected by analyzing the results: 1. The gain should be 1 at the center frequency of \(15\mathrm{kHz}\) (0 dB in the frequency response graph). 2. The 3-dB bandwidth of the filter should be \(\frac{f_c}{Q}=\frac{15\mathrm{kHz}}{10}=1.5\mathrm{kHz}\). This means the output gain should be 3 dB less at the lower and upper frequencies \(15\mathrm{kHz} \pm 0.75\mathrm{kHz}\).
05

Adjusting the filter design if necessary

If the simulation results do not match the given specifications, review the filter design and component values. Adjust them if necessary, and run the simulation again to verify the performance of the inverting band-pass filter. Repeat this step until the desired filter characteristics are achieved.

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