Understanding the Choke-Input Filter for Power Supply Applications

Historical Use:
- Previously widely used
- Less common now due to cost, bulk, and weight
- Useful for understanding other filters
AC source drives current through:
- Inductor, Capacitor, and Resistor
Reactance equations:
- Inductive Reactance and Capacitive Reactance:

\[X_L = 2 \pi f L \qquad X_C = \frac{1}{2 \pi f C}\]

Choke Characteristics:
- Opposes change in current
- Ideally reduces AC current in load resistor to zero

Design Requirement 1:
- \(X_C\) at input frequency much smaller than \(R_L\)
- Allows ignoring load resistance; see equivalent circuit (Figure b)
Design Requirement 2:
- \(X_L\) much greater than \(X_C\) at input frequency
- AC output voltage approaches zero
DC Current:
- Choke approximates short circuit at 0 Hz
- Capacitor approximates open at 0 Hz
- DC current passes to load with minimal loss

Circuit behaves as a reactive voltage divider
When \(X_L \gg X_C\):
- Almost all AC voltage is dropped across the choke
- AC output voltage:

\[V_{\text{out}} \approx \frac{X_C}{X_L} V_{\text{in}}\]

Given:
- \(X_L = 10 \text{ k}\Omega\), \(X_C = 100 \Omega\), \(V_{\text{in}} = 15 \text{ V}\)
\[V_{\text{out}} \approx \frac{100 \Omega}{10 \text{ k}\Omega} \times 15 \text{ V} = 0.15 \text{ V}\]
AC output voltage calculation:
The filter reduces the AC voltage by a factor of 100

SECTION 01

Filtering the Output of a Rectifier

Choke-Input Filter:
- Connects rectifier to load (half-wave, full-wave, bridge)
- Uses superposition theorem:
  - Analyze each source separately
  - Combine voltages for total result
- Rectifier output components:
  - DC voltage (average value)
  - AC voltage (fluctuating part)

AC voltage across load resistor:
- \(X_L \gg X_C\)
- Minimal AC voltage across load
- AC component approximated by Eq.

\[V_{\text{out}} \approx \frac{X_C}{X_L} V_{\text{in}}\]

DC voltage considerations:
- At 0 Hz: \(X_L = 0\), \(X_C = \infty\)
- Series resistance of inductor (\(R_S\)) \(<<\) load resistor (\(R_L\))

Output:
- DC component passed to load
- AC component blocked (ripple)
- Ripple measured with oscilloscope (AC coupling)
Main Disadvantage
- Power supply converts AC to DC
- Trend towards low-voltage, high-current supplies
- Line frequency (60 Hz) requires large inductors:
  - Large inductors have high winding resistance
  - Causes significant DC voltage drop
  - Bulkiness unsuitable for lightweight semiconductor circuits
Application of choke-input filter: Switching Regulators
- Used in computers, monitors, and various equipment
- Operates at frequencies \(>\) 20 kHz
- Allows use of smaller inductors for filtering