** LEAD Circuit** is an important circuit that can be added to control systems in order to increase the system's stability.

### What effect does the LEAD circuit have on the system?

When added to the system, the ** LEAD circuit** provides a convenient way to move a certain pole to the left. Therefore; increasing the system's stability. I have talked in a previous summary about the effects of pole locations on the stability of the system. You can read that summary

**here**.

### Drawbacks of adding a LEAD circuit to the system

Even though moving poles to the left makes the system more stable, it makes the system slower and decreases the accuracy.

### Where do we add the LEAD circuit?

** LEAD Circuit** is always added in the low power section just before the system. This is because if the

**was added in the high power section, high power resistances and capacitors will be needed when designing the**

*LEAD Circuit***.**

*LEAD circuit*### Diagram of LEAD circuit

### Deducing the Transfer Function (TF) of LEAD circuit (4 steps)

- Change the
from*LEAD Circuit*to*t-domain*(*Laplace domain*) according to the following:*S-domain*

Therefore; thebecomes:*LEAD circuit* - Find the Input Resistance

### Example

Design a suitable circuit to remove the old pole (S+2) in the following control system by replacing it with a new pole (S+4). Sketch the circuit indicating whether it is LEAD OR LAG, and derive its ** Transfer Function** TF. Finally, find the values of R1, R2, and C?

It is clear from the designed circuit that b = 4 > a = 2. Therefore; the designed circuit is a ** LEAD Circuit**. Also notice how the
pole (-2) was replaced by the pole (-4)

Finding the values of R1, R2, and C

**Note:** If the resulting values of R2 and C are illogic or don't exist on the market, we assume another value for R1 and repeat calculations. Therefore; it is highly recommended that you do all the calculations in an EXCEL spreadsheet.

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