Filter design example

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.

Fig. 1Active RC integrator^[1]

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.

Fig. 2Active RC adder^[1]

From Fig. 2, we have:

Therefore,

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

Fig. 3Active RC scaler^[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.

Fig. 4SFG - signal flow graph^[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:

Fig. 5Redrawn SFG based on the three basic building blocks^[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.

Fig. 6Verification of the actual filter implementation in SIMetrix

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

Fig. 7Verification of the actual filter implementation in SIMetrix

References and downloads

[1] EEE598 - by Prof. Hongjiang Song

[2] Prof. Hongjiang Song

[3] Prof. Hongjiang Song's LinkedIn

[4] Filter test bench in SIMetrix - pdf

[5] Filter test bench in SIMetrix - download