Determining component values for tone control circuit

[mememe653]

Homework Statement

Your tone control circuit must satisfy the following specifications:
1. peak input signal voltage of 8 V;
2. peak output signal voltage of 8 V;
3. operating frequency range of 20 Hz – 20 kHz (audio band);
4. three tone bands with cut-off frequencies at 200 Hz and 2 kHz (± 10%);
5. variable gain control (± 6 dB) for each band;
6. input impedance of at least 10 kΩ;
7. output impedance of at most 1 kΩ.

There are 4 main stages in our tone control:
High-pass filter
Low-pass filter
Summing amplifier for mid-band
Summing amplifier with variable gain for each band

Tone control circuit schematic is attached.

Before you can embark on the construction of your tone control circuit, you must first determine the value of the components to populate the PCB. Schematic of the overall circuit is shown in Figure 2. A full-sized PDF of this schematic is available from the course site on MyUni.
Proceed with the following steps:
1. Determine the minimum input impedance of each stage. This will be the lower limit for your resistor values (especially applicable to the complex input impedance of the high-pass filter).
2. Determine the input impedance of the op-amps. We want our resistors to be much lower
than the input impedance, so ideally choose the upper limit of the resistors to be 100 times smaller. You are recommended to check up the op-amps’ input impedances from the datasheet, available on MyUni. However, it is possible that we might not meet the upper limit due to Step 1, and need to relax this limit. Discuss how this can affect your design.
3. Determine the input bypass capacitor C1.
4. Calculate the components for low-pass filter: R1, R2, C2.
5. Calculate the components for high-pass: R3, R4, C3.
6. Determine the components for mid-band summing amp: R5 – R8.
7. Determine the components for variable gain summing amp: R9 – R12.
8. Calculate the required capacitor for the final low-pass filter: C4 (What criterion will you use in choosing this value?)

NOTE: I don't want you to do steps 1-8 above for me as I don't want to plagiarise; my problem is simply that I am stuck on step 1.

Homework Equations

The filters we are designing are based on active first-order Butterworth filters using op-amps. The generic design of the filter is the same for the high-pass and the low-pass filters as we are using the op-amps in the inverting amplifier configuration (Table 1). In this configuration, the gain of the amplifier is given by:
Vo/Vi = -Zb/Za
where Vo and Vi are the input and output voltages (s-domain), and the input impedance is
=
due to the inverting input being a virtual ground. The output impedance is governed by the op-amp that we use. By using the following table, you can specify appropriate values for R and C for the low- and high-pass filters, respectively.

The table is attached in 2 parts.

The other information (not shown in the attachments) in the table is:
Input impedance Zi = R1 Zi = R1+(1/(jwC1))
Output impedance Zo ≈ 70Ω Zo ≈ 70Ω

Also, all potentiometers in the circuit are 20kΩ.

There are two summing amplifiers required in this circuit, based on the same schematic as shown in Figure 1 (this paragraph is likely irrelevant, but you can see the schematic of the summing amplifiers by just finding them in the attached tone control circuit schematic; Figure 1 is not attached). The first amplifier is a 3-input unity gain summing amplifier that combines the input signal with the high-pass and low-pass outputs to obtain the mid-band. The second amplifier is a 3-input variable gain summing amplifier. It needs to provide the (+/- 6 dB) gain control for each audio band that we require for this project. For the variable gain second summing amplifier, you will need to work out the range of the variable resistance to produce gains ranging from -6 dB to +6 dB.

The Attempt at a Solution

I am stuck on step 1 of determining the values of the components to populate the PCB. This is because it seems to me that there is no specification for the minimum input impedance of each stage, thus my best attempt at a solution would be to suggest that we use 10kΩ as the minimum input impedance of each stage despite it rather being the tone control circuit as a whole which is specified to have input impedance ≥ 10kΩ, so this is surely wrong...

I simply need to know how to complete this first step so that I can proceed to do the other steps in the design by myself.

Is there sufficient information provided to determine the minimum input impedance of each stage and thus complete step 1?

A reply ASAP would be much appreciated because this component value design is due very soon and I can't really start it until I can complete the first step! I tried to contact the person in charge of this piece of work that's been set, well in advance of the due date, but they have not replied.

Thanks

 

[KataKoniK]

for your help.





Dear ,

Thank you for reaching out for help with your tone control circuit design. I am happy to assist you in completing step 1 and providing guidance for the rest of the steps.

After reviewing the specifications of the tone control circuit, it appears that there is indeed no specific requirement for the minimum input impedance of each stage. However, we can make some assumptions and use some general guidelines to determine a suitable minimum input impedance for each stage.

Firstly, it is important to note that the overall input impedance of the tone control circuit must be at least 10 kΩ. This means that the input impedance of each stage should be at least 10 kΩ, as you have correctly stated. However, it is also important to consider the input impedance of the op-amps used in the circuit.

Based on the information provided, the input impedance of the op-amps is not specified. However, it is common for op-amps to have input impedances in the range of hundreds of kΩ to a few MΩ. Therefore, we can assume that the input impedance of the op-amps used in this circuit will be in this range.

With this in mind, we can use the guideline of having the input impedance of each stage be at least 100 times smaller than the input impedance of the op-amps. This will ensure that the resistors used in the circuit will have a much lower impedance than the op-amps, allowing for accurate control of the input signal.

In summary, a suitable minimum input impedance for each stage would be at least 10 kΩ, but ideally closer to 100 kΩ to ensure that the resistors have a much lower impedance than the op-amps.

I hope this helps you to complete step 1 and proceed with the rest of the design. If you have any further questions or concerns, please do not hesitate to reach out for assistance.