**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:

\(X_L = 10 \text{ k}\Omega\), \(X_C = 100 \Omega\), \(V_{\text{in}} = 15 \text{ V}\)

AC output voltage calculation: \[V_{\text{out}} \approx \frac{100 \Omega}{10 \text{ k}\Omega} \times 15 \text{ V} = 0.15 \text{ V}\]

The filter reduces the AC voltage by a factor of 100

**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