1. Lecture 7: First Order Filter and Bode Plot
Jeong Wan Lee
전기회로이론 및 실험

2. First Order Filters
* Filters: remove unwanted information from a signal.
* Example:
remove unwanted 60 Hz noise (caused by a power supply).
* A first order (passive) filter, R C C
Vin
Vin R
Vout
Vout
High Pass Filter
Low Pass Filter

3. High Pass Filter * High pass filter: allows high frequencies to pass
and blocks low frequencies.
* Analysis Methods
Two Responses:
1) voltage transfer function. C
Vin R
Vout
2) power transfer function.

4. Power Transfer function
=> The power transfer function can be rewritten as:
* transfer function of the high pass filter circuit: Vout/Vin ?
- impedance of the capacitor and resister
and
- voltage divider equation

5. Cont... - Rearranging this equation we get: Comments
i) When the frequency is low (i.e.  is small):
the output voltage will be zero.
ii) At higher frequencies:
the output voltage will be equal to the input voltage.

6. The decibel (dB) Unit Definition: Or
i) For TP > 0 we have a gain (i.e. Vout > Vin).
ii) For TP < 0 we have an attenuation (i.e. Vout < Vin).
iii) A 0 dB gain means that Vout=Vin.

7. Simple High Pass Filter 1C
Vin R
Vout
Transfer Function:
and
The breakpoint or 3dB point:
or when

8. Simple High Pass Filter 2
Vin L
Vout
and
The breakpoint or 3dB point:
or when

9. Simple Low Pass Filter 1 Transfer Function:
Vin
Vout
Transfer Function:
and
The breakpoint or 3dB point:
or when

10. Simple Low Pass Filter 2 The breakpoint or 3dB point: L Vin R Vout and
or when

11. Bode Plots for Gain
* Bode Plot for Gain: frequency (x-axis) verses Gain (y-axis).
- Uses semi log scale
- Frequency on the logarithmic x-axis.
- Gain on the y-axis as the dB scale
Voltage gain:
Power Gain:

12. Bode Plots for Phase...
* Bode Plot for Phase: frequency (x-axis) verses Phaes (y-axis)
- Uses semi log scale
- Frequency on the logarithmic x-axis.
- Phaes on the y-axis as the Degree scale
Example: first order low pass filter using the capacitor.
Transfer Function R C
Vin
Vout
For frequencies below the
breakpoint (or 3dB point),
=> RC is much less that 1.

13. Cont...
If RC << 1, then the transfer function can be approximated to:
phase = 00.
frequencies At the breakpoint (or 3dB point), => RC = 1.
and thus

14. Bode Plots for Phase...
multiply the top and bottom of this equation by (1-j)
Phase:

15. Cont... For frequencies well above the 3dB point wRC > 1,
Multiplying top and bottom by j we get
=> Phaes: -900.

16. Complete Response (Magnitude and Phase)
0dB
-10dB
-20dB 1 10 10
102
103
103
104
105 00
Assuming a 3dB point of around
200 rads/s
-450
-900 1 10
102 10
103
104
105

17. Help Sheet - Complex Numbers
a+jb => M. Im a M b  Re