# Filter design example

Ming Sun / December 25, 2022

9 min read • ––– views

## Background

The techniques described in this blog post is based on the class and materials taught by Prof. Hongjiang Song at ASU EEE598 Serial link class. Please refer to **Ref. [1]** for more detailed information about the class.

## Design target

The design target is to use the above techniques to design a circuit which will have the following transfer function:

## Building blocks

In this section, we are going to make several building blocks with **active-RC** circuit.

- Integrator
**G**. Let us first make an integrator building block with the following transfer function:

**Fig. 1** shows an integrator by using the active RC circuit.

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Let us try to derive the transfer function for **Fig. 1**. We have:

Therefore, we have:

Where,

- Adder.
**Fig. 2**shows an adder created by the active RC circuit.

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From **Fig. 2**, we have:

Therefore,

- Scaler.
**Fig. 3**shows an scaler (gain block) created by the active RC circuit.

^{[1]}

From **Fig. 3**, we have:

Therefore, we have:

## Filter design based on signal flow chart

By combining **Eq. 1** and **Eq. 2**, we have:

**Eq. 10** can be rewritten as:

Or,

**Eq. 12** can be further written as:

The signal flow chart can be drawn based on **Eq. 13**, which is as shown in **Fig. 4**.

^{[1]}

From **Fig. 4**, we have:

Which matches exactly with **Eq. 13**.

Since we have three basic building blocks (integrator, adder and scaler), **Fig. 4** can be re-drawn as:

^{[1]}

Let us pick **R=100kΩ** and **C=100pF**. As a result,

## Verification

The test bench is as shown in **Fig. 6**. We have an active RC circuit and a Laplace transfer function block so that we can compare the Bode plot between the actual circuits and the Math equations.

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The Bode plot from SIMetrix AC simulation is as shown in **Fig. 7**.

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## References and downloads

[1] EEE598 - by Prof. Hongjiang Song

[3] Prof. Hongjiang Song's LinkedIn