Project: Spectrum – Filter Design

Frequency Response

As I said in the previous post, I want my filters to perform in the same way as the MSGEQ7. The frequency response of this chip is given in it’s datasheet.

MSGEQ7_Frequency_response.png

The 7 frequency band responses of the MSGEQ7

From the datasheet I can see that, to replicate this response, I will need 7 bandpass filters at 63Hz, 160Hz, 400Hz, 1kHz, 2.5kHz, 6.25kHz and 16kHz. Each filter will need a quality factor of 6 (this basically sets the bandwidth of the filter).

To create these band pass filters I will use a Multiple-Feedback Bandpass filter circuit.

OPtBaPass.png

Multiple-Feedback Bandpass Filter

To help me choose component values for my filters I used an online calculator. This resulted in the following values.

Frequency R1 R2 R3 C1 C2
63Hz 4.7k‎Ω 1.1k‎Ω 150k‎Ω 0.33uF 0.15uF
160Hz 6.2k‎Ω 1.3k‎Ω 180k‎Ω 0.1uF 0.047uF
400Hz 5.1k‎Ω 1.2k‎Ω 160k‎Ω 0.047uF 0.022uF
1kHz 4.3k‎Ω 1.2k‎Ω 180k‎Ω 0.022uF 0.0068uF
2.5kHz 5.6k‎Ω 1.3k‎Ω 180k‎Ω 0.0068uF 0.0033uF
6.25kHz 4.7k‎Ω 1.1k‎Ω 150k‎Ω 0.0033uF 0.0015uF
16kHz 6.2k‎Ω 1.3k‎Ω 180k‎Ω 0.001uF 470pF

However, I’m not going to trust the calculator without validating the design. The first thing I need to do is calculate the frequency response of an arbitrary Multiple-Feedback Bandpass filter.

Transfer_Function_Calculations.png

My derivation of the transfer function of the filter

Using Matlab I simulated the frequency response of the 63Hz filter using the equation I derived above:

Filter1_Matlab_Frequency_Respnse.png

The frequency response that I derived, simulated in Matlab

I then created the circuit in LTSpice and simulated the frequency response of the filter directly:

Filter1_LTSpice_Frequency_Respnse.png

The frequency response of the filter, simulated in LTSpice

Filter1_LTSpice_Model

The circuit model in LTSpice

As you can see, the two frequency responses are the same and so I am happy that my equation accurately describes the frequency response of the real circuit.

Using Matlab, I simulated the 7 circuits simultaneously using the transfer function I derived.

filters

The simulated frequency response of the 7 bandpass filters

This matches well with the frequency response of the MSGEQ7 shown above and so I am happy with this set of filters.

Input Impedance

I also need to know what the input impedance of each filter is so that I can verify that when I put 7 of the filters in parallel, the input impedance will be significantly greater than the output impedance of my amplifier stage.

Rin_Derivation

My derivation of the input impedance in terms of the component values and gain

Using Matlab I simulated the input impedance of the 63Hz filter using the equation I derived above:

Filter1_Sim_Matlab_Rin.png

The input impedance according to my equation, simulated in Matlab

I then used my LTSpice model to simulate the input impedance of the filter directly:

Filter1_Sim_LTSpice_Rin.png

The input impedance of the filter, simulated in LTSpice

As you can see, the two input impedances are the same and so I am happy that my equation accurately describes the input impedance of the real circuit.

I then simulated the input impedance of all 7 filters at once:

Parallel_Rin_Sim_Matlab.png

The 7 input impedances, and the resulting parallel impedance of all 7 filters.

Parallel_Rin_Sim_Matlab2.png

Parallel impedance of all 7 filters

This plot shows that the lowest parallel impedance is about 677Ω and occurs at about 6.5kHz. This is a couple of orders of magnitude greater than that of my amplifier stage which I expect to be in the single digits.

Summary

This validation has shown that the frequency response of the filters is correct and that the input impedance of all 7 filters in parallel is sufficiently high. Therefore I am happy with this design.

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