# Ideal and Typical Power Switching Waveforms

Power electronics rely heavily on efficient switching, but how does this translate to real-world applications? This article explores the ideal and typical waveforms of power switches, their operation, and the associated power losses.

## Ideal Power Switching Waveforms

An ideal power device can control power flow without power dissipation. Here are the key characteristics:

• Zero Power Dissipation: An ideal power switch can operate without any power loss.
• Inductive Loads: Motors and solenoids
• Resistive Loads: Heaters and lamp filaments
• Capacitive Loads: Transducers and LCD displays
• Pulsed Control: Power is often delivered through periodic turning on and off of the device.

### Characteristics of Ideal Waveforms

• The switch remains on for a time interval of tON and off for the remainder of the cycle, denoted as T.
• On-State Voltage Drop: For an ideal switch, the voltage drop during the on-state is zero, resulting in no power dissipation.
• Off-State Leakage Current: During the off-state, the leakage current is also zero, leading to no power loss.
• Instantaneous Transitions: Transitions between the on-state and off-state occur instantaneously, causing no power loss.

## Typical Power Switching Waveforms

Typical power switches differ from ideal devices and exhibit power dissipation during various states of operation.

### Power Dissipation in the On-State

• Voltage Drop ((V_F)): A typical switch has a non-zero voltage drop during the on-state.
• Power Dissipation Formula:
$$P_L(on) = \delta \cdot I_F \cdot V_F$$
• Where:
• (I_F) = On-state current
• (\delta) = Duty cycle, calculated as:
$$\delta = \frac{t_1}{T}$$
• (T) = Time period (the reciprocal of operating frequency)

### Power Dissipation in the Off-State

• Leakage Current ((I_L)): In the off-state, a leakage current exists which contributes to power dissipation.
• Power Dissipation Formula:
$$P_L(off) = (1 – \delta) \cdot I_L \cdot V_R$$
• Where:
• (V_R) = Reverse bias voltage
• Alternative Formula for Long Switching Times:
$$P_L(off) = \frac{(t_4 – t_3) \cdot I_L \cdot V_R}{T}$$

### Considerations

• Negligible Off-State Losses: Typically, power dissipation in the off-state is small compared to other losses and can often be neglected.
• Impact of Temperature: At elevated temperatures or with Schottky contacts, off-state losses may become significant.

## Power Dissipation During Switching

Power dissipation must be analyzed separately for turn-off and turn-on transients.

### Turn-Off Transient

For inductive loads, the voltage across the switch rapidly increases to the DC supply voltage while the current decreases.

• Power Loss Formula:
$$P_L(turn_off) = 0.5 \cdot (t_3 – t_1) \cdot I_F \cdot V_R \cdot f$$
• Where:
• (f) = Operating frequency

### Turn-On Transient

The power loss during the turn-on transition is analyzed similarly.

• Power Loss Formula:
$$P_L(turn_on) = 0.5 \cdot (t_6 – t_4) \cdot I_F \cdot V_R \cdot f$$

### Total Power Dissipation

The total power dissipation in the switch combines all components:
$$P_L(total) = P_L(on) + P_L(off) + P_L(turn_off) + P_L(turn_on)$$

### Frequency Considerations

• Low Operating Frequencies: At low frequencies, the on-state power loss is usually dominant, emphasizing the need for switches with low on-state voltage drops.
• High Operating Frequencies: At high frequencies, switching losses become more significant, leading to a demand for fast-switching devices with minimal transition times.

## Conclusion

As power switch technology evolves, the overall power loss in optimized designs continues to decrease. This progress enhances the efficiency of power systems.