09 rc filters
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This document discusses different types of filters, including RC filters, active filters, and higher order filters. It provides information on passive and active low-pass, high-pass, band-pass, and band-reject filters. Key points covered include the properties and design of different filter types, such as using capacitors and resistors to construct simple RC filters, and employing op-amps to create active filters that can amplify signals during the filtering process. Higher order filters are discussed as providing closer approximations to ideal filter characteristics. Design guidelines and examples are provided for low-pass and high-pass active filters.
09 rc filters
- 1. 9-1 Lecture 9 RC Filters 9-2 Outlines of Filter Design Filter input output Filtering: Certain desirable features are retained Other undesirable features are suppressed
- 2. 9-3 Filters Filters have the property of removing unwanted frequencies from our signal. Classes: Passive (made of capacitors, resistors, inductors) Active (involving an amplifier) Types: Low-Pass (remove high frequencies) High-Pass (remove low frequencies or DC) Band-Pass (remove a range of frequencies on two sides) Notch (removes frequencies in the middle) 9-4 Classification of Filters Signal Filter Analog Filter Digital Filter Element Type Frequency Band Active Passive Low-Pass High-Pass Band-Pass Band-Reject All-Pass
- 3. 9-5 Filters – Type of filters http://www.ece.eps.hw.ac.uk/~pmr/teaching/ae/lectures/circuits1.htm Passive filters 9-6 Terminology in Filter Design • Signal-To-Noise Ratio (S/N) • Bandwidth the range of frequencies of |G(jw)|>0.707 • Cutoff Frequency the end of pass-band frequency • Break-point of a filter the point with a gain of -3dB dB W W N S N S ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⋅= log10
- 4. 9-7 RC Filters In combination with a resistor, a capacitor’s variation in reactance with frequency can be used to construct a simple low-pass or high-pass filter: R RC C Vin Vout Vin Vout High-pass filter Low-pass filter fC X XRZ Z R VV C C π2 1 22 inout = += ⋅= fC X XRZ Z X VV C C C π2 1 22 inout = += ⋅= 9-8 Passive Low-Pass Filter • The pass-band is from 0 to some frequency wp. • Its stop-band extends form some frequency ws, to infinity. • In practical circuit design, engineers often choose amplitude gain of 0.95 for passive RC filters: ωωp ωs )( ωjH Vout Vin C R VVoutoutVVinin RL
- 5. 9-9 Passive High-Pass Filter • Its stop-band is form 0 to some frequency ws • The pass-band is from some frequency wp to infinity. • In practical circuit design, engineers choose amplitude gain of 0.95 for passive CR filters: ωωs ωp )( ωjH Vout Vin R C VVoutoutVVinin 9-10 Design of Passive Filters ( ) 1 1 + = ω ω jRC jH ( ) 1 1 + = RCs sH Transfer Function ( )2 1 1 ωRCV V in out + = The amplitude response: πτπ 2 1 2 1 3 == RC f dB The 3dB break-point is at: LF L ZZ Z G + = The amplitude gain: C R VVoutoutVVinin RL
- 6. 9-11 Guideline of Pass Filter Design R ( ) 1 1 + = s sH τ Transfer Function C VVoutoutVVinin RL RC=τ Time Constant Select resistor based on amplitude gain: 95.0= + = LF L ZZ Z G LLF RZRZ ⋅==≈ 053.0 95.0 05.0 Select capacitor based on cut-off freq: dBRfR C 32 1 π τ == 9-12 Higher Order Filters C R VVoutoutVVinin First Order RC Low Pass Second Order RC Low Pass C2 VVoutoutVVinin C1 R1 R2 The higher the order of the filter, the closer it approaches ideal characteristics.
- 7. 9-13 Active Filters • Active filters employ Op-Amps to attenuate select frequencies and amplify signal during filtering process. • Q factor of a filter is defined as the ratio of the center frequency fc to the bandwidth fH - fL : ( )LH C ff f Q − = 9-14 Active filters- cascading low pass filters First order Op Amp for everyone, Ron Mancini, Ed, Texas instrument, 2001. Second order 3rd order 5th order
- 8. 9-15 Low-Pass Active Filter + - R1 RF R2 C1 C2 Passive filters take up lots of space in a circuit and cause signal to be lost. Combining a passive RC filter with an op amp for amplification creates what is known as an active filter. By “active” we mean that the filter requires power to operate. Here is an example of an active low-pass filter. The signal is provided to the noninverted input through an RC low-pass filter made up of R2 and C2. Feedback to limit gain comes through C1 and RF. The parallel combination of C1 and RF presents an impedance which decreases with increasing frequency, meaning that more negative feedback is provided to the inverting input at higher frequencies, reducing gain at those frequencies. 9-16 Design of Low Pass Active Filters Example: Design a low pass filter with cut-off frequency of 5 kHz, and DC gain of 10: Two equations, three unknowns - + Vin Vout R1 RF A B C2 Transfer Function: 0 0 .. ω ω + = s KFT LP ( )22 1 CR f F H π= The -3 dB cut-off frequency: 1R R K F LP −= The DC gain:
- 9. 9-17 High-Pass Active Filter + - R1 RF R2 C1 C2 R3 Here is an example of an active high-pass filter. C2 and R2 make up an RC high-pass filter at the input of the op amp. R3 provides a path for the input when the frequency is too low for C2 to freely conduct. When the input signal passes through R3 instead of into the amplifier, the output is tied directly to the input and the gain is reduced. So, this amplifier has low gain at low frequencies and higher gain at high frequencies. C1 prevent any DC at the input from being coupled to the output. 9-18 Design of High Pass Active Filters Vout - + Vin R1 RF A B C1 The -3 dB cut-off frequency: The DC gain: Two equations, three unknowns Select one component based on other conditions, and determine the values of the other two components. ( )112 1 CR fH π= 1R R K F HP = Transfer Function: 0 .. ω+ = s s KFT HP
- 10. 9-19 Filter Class • A filter of a given order can be made to approximate to ideal characteristics in a number of ways, depending on the values of the filter components (or say: depending on the filter class. • Two useful classes are Butterworth (maximally flat) and Chebyshev (equal-ripple) filters (n is the filter order) n C in out f fV V 2 1 1 ⎟ ⎠ ⎞⎜ ⎝ ⎛+ =Butterworth Filter Chebyshev Filter ⎟ ⎠ ⎞⎜ ⎝ ⎛+ = C n in out f fCE V V 22 1 1 9-20 Higher Order Active Filters Vout - + Vin R2 Rb C1 R1 Ra C2 Gain=K Filter Class R1 R2 C1 C2 K Buterworth 3.01 dB at ωH 1.00 1.00 1.00 1.00 1.59 Chebyshev 1 dB ripple 1.00 1.00 0.94 0.97 2.00 The above list gives the gain and component valves for one of the many choices for ωH=1. You may find more combinations from filter design handbook(s).
- 11. 9-21 Active Filters– High Pass Filters Op Amp for everyone, Ron Mancini, Ed, Texas instrument, 2001. High passLow pass 9-22 Active Filters – Band Pass Filter Op Amp for everyone, Ron Mancini, Ed, Texas instrument, 2001.
- 12. 9-23 Active Filters – Band Reject Filter Op Amp for everyone, Ron Mancini, Ed, Texas instrument, 2001. Passive band reject filter Active band reject filter 9-24 References • Op Amp for everyone, Ron Mancini, Ed, Texas instrument, 2001.