Introduction:
A phase lead compensating network is used to improve the transient response and stability of a control system. It introduces a phase lead in the frequency response of the system. This can be achieved by adding a pole and a zero in the s-plane. The locations of the pole and zero determine the amount of phase lead introduced.

Conditions for a Phase Lead Compensating Network:
To design a phase lead compensating network, the following conditions must be satisfied:

1. Pole Location:
The pole of the compensating network, PC, should be located to the left of the zero to ensure stability. This means that the real part of the pole should be negative. If the pole is located to the right of the zero, it will introduce a phase lag instead of a phase lead, which is undesirable.

2. Zero Location:
The zero of the compensating network, ZC, should be located to the left of the pole, PC. This ensures that the compensating network introduces a phase lead. If the zero is located to the right of the pole, it will introduce a phase lag, which is not desired.

3. Magnitude Ratio:
The magnitude ratio between the pole and zero, |PC/ZC|, determines the amount of phase lead introduced. A larger magnitude ratio will result in a larger phase lead. It is typically chosen based on the desired phase margin and system requirements.

4. Phase Lead Angle:
The phase lead angle introduced by the compensating network is given by the angle between the pole and zero, θ = atan(ωZC) - atan(ωPC), where ω is the frequency. The phase lead angle should be chosen based on the desired phase margin and system requirements.

Summary:
To design a phase lead compensating network, the pole should be located to the left of the zero, and both should have negative real parts. The magnitude ratio between the pole and zero determines the amount of phase lead introduced, while the phase lead angle is determined by the difference in angles between the pole and zero. These conditions ensure stability and introduce the desired phase lead in the control system.