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
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