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

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

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.

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

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.

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.

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

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

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

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

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:

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.

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

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

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

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

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