# Lecture 18

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### Lecture 18 Bode Plot, High Pass Filter, Series Resonance:

Lecture 18 Bode Plot, High Pass Filter, Series Resonance

### :

First-Order Low Pass Filter

### Bode Plot for a First-Order Low-Pass Filter:

Bode Plot for a First-Order Low-Pass Filter A Bode plot shows the magnitude of a network function in decibels versus frequency using a logarithmic scale for frequency.

### Bode Plot for a First-Order Low-Pass Filter:

Bode Plot for a First-Order Low-Pass Filter

### Asymptotic Behavior of Magnitude for Low and High Frequencies:

Asymptotic Behavior of Magnitude for Low and High Frequencies

### Magnitude Bode Plot for First-Order Low Pass Filter:

Magnitude Bode Plot for First-Order Low Pass Filter

### Asymptotic Behavior of Phase for Low and High Frequencies:

Asymptotic Behavior of Phase for Low and High Frequencies

### PowerPoint Presentation:

A horizontal line at zero for f < f B / 10. 2. A sloping line from zero phase at f B / 10 to –90° at 10 f B . 3. A horizontal line at –90° for f > 10 f B .

### Exercise 6.11:

Exercise 6.11 Sketch the Bode plots for the low-pass filter shown above:

Exercise 6.11

### First-Order High-Pass Filter:

First-Order High-Pass Filter

### First-Order High-Pass Filter:

First-Order High-Pass Filter

### First-Order High-Pass Filter:

First-Order High-Pass Filter

### First-Order High-Pass Filter:

First-Order High-Pass Filter

### Asymptotic Behavior of First-Order High-Pass Filter:

Asymptotic Behavior of First-Order High-Pass Filter

### Bode Plots for the First-Order High-Pass Filter:

Bode Plots for the First-Order High-Pass Filter

### Exercise 6.13:

Exercise 6.13 Find the transfer function for this circuit:

### Exercise 6.14:

Exercise 6.14 Find the half power frequency and the capacitance for a high-pass filter that reduces the amplitude of a frequency component at 1 kHz by 50dB R=1k 

### Exercise 6.14:

Exercise 6.14 What half-power frequency f B is 2.5 decades above 1 kHz?

Exercise 6.14

### Computer-Generated Bode Plot:

Computer-Generated Bode Plot

### Computer-Generated Bode Plot:

Computer-Generated Bode Plot Check the low and high frequency behavior to make sure the computer generated Bode plot is correct

### Low Frequency Behavior:

Low Frequency Behavior At low frequency the inductance is a short circuit The capacitance is an open circuit

### Low Frequency Behavior:

Low Frequency Behavior

### High Frequency Behavior:

High Frequency Behavior At high frequency the inductance is an open circuit The capacitance is a short circuit

### High Frequency Behavior:

High Frequency Behavior

MATLAB Code

MATLAB Output

### Resonance:

Resonance Resonance is a phenomenon that can be observed in mechanical systems and electrical circuits.

### Series Resonance:

Series Resonance http://www.intuitor.com/resonance/circuits.html

### Series Resonance:

Series Resonance http://www.intuitor.com/resonance/circuits.html

### Series Resonance:

Series Resonance http://www.intuitor.com/resonance/circuits.html

### Series Resonance:

Series Resonance http://www.intuitor.com/resonance/circuits.html

### Series Resonance:

Series Resonance http://www.intuitor.com/resonance/circuits.html

### Series Resonance:

Series Resonance For resonance the reactance of the inductor and the capacitor cancel:

### Series Resonance:

Series Resonance Quality factor Q S

Series Resonance

### Series Resonance:

Series Resonance 