APP0 University of alifornia Berkeley ollege of Engineering Department of Electrical Engineering and omputer Science obert W. Brodersen EES40 Analog ircuit Design t ISE Lectures on APPLIATINS t FALL.0V V 0.99V APP0 APP03 50 Years Ago 0dB Telephone Filter A/D onverter PM odec 40dB 60Hz 800Hz 3.4kHz 5.8kHz
Pole Zero Diagrams A convenient way of visualizing transfer functions, the Laplace Transform : ν UT ( s) ( ) ( s) H S ν IN ( s z ) ( s z ) ( s p ) ( s p ) APP04 ften what we are really interested in is magnitude and phase at frequency, H( s) S j ω Poles Zero Diagrams (ont.) ω.,i.e. the APP05 p 0 j 30π p 0 j 30π j ω z j 0π σ z j 0π S PLANE S σ j ω ( j ω z ) ( j ω z ) ( j ω p ) ( j ω p ) To find the magnitude use the fact that magnitude of the products equals the product of the magnitudes, so that : ( j ω z ) ( j ω z ) ( j ω p ) ( j ω p ) ( j ω z ) ( j ω z ) ( j ω p ) ( j ω p ) Poles Zero Diagrams (ont.) APP06 Poles Zero Diagrams (ont.) APP07 ( j ω ) p ( j ω p ) j ω ( j ω z ) σ ( j ω z ) Lets graphically evaluate here at jω j40π S PLANE S σ j ω ω Z jω σ 0dB The magnitude 3 & 4 divided by the is the product of the lengths of vectors product of the lengths of vectors &. 40dB 60Hz 800Hz 3.4kHz 5.8kHz
Poles Zero Diagrams (ont.) APP08 Poles Zero Diagrams (ont.) APP09 p 3 jω σ 0dB p 3 f 3dB f f 40dB 60Hz 800Hz 3.4kHz 5.8kHz f Filter Design Specification APP0 APP AMPL db FE Active Filter (ontinuous Time) L Prototypes ontinuous Time Factorization into Pole,Zero sections (Biquadratic) Switched apacitor ircuits (Sampled Data any Amplitude) hose an Equivalent discrete time structure. Use appropriate cont. Discrete Transformation (i.e. Bilinear, Mapping differentials) Σ z Simulate Disirete Time inplementation and compare with original spec.(dinap) Digital Filter (Sampled Data, uantized Amplitude) α
APP Typical Filter Specifications APP3 ontinuous time specifications of transfer function H(ω) AMPL ( ω) ( ω) e j θω ν UT ν IN ( db ) FE Digital Filter A/D Amplitude (Magnitude in db) 0log[ H ( ω ) H ( ω) ] Typical Filter Specifications (ont.) APP4 Types of Pole Transfer Functions APP5 Lowpass : Group Delay (msec.) Group Delay θ( ω) ω H( s) ωo s ω o s FE Group Delay jω P ω P j ω P σ P s, s ωo 4 ωo
Types of Pole Transfer Functions (ont.) ( Lowpass ) APP6 Bandpass : H( s) Types of Pole Transfer Functions (ont.) s s ω o s jω P APP7 ω o 0.707 σ P s P ω P s P s P s P ω P s P ωo Types of Pole Transfer Functions (ont.) Highpass : APP8 Types of Pole Transfer Functions (ont.) APP9 Bandstop (or Notch) : Highpass ( Lowpass) ( Bandpass) ω o s s ω o s ω o s s ω o s ωo jω P s Bandstop s ω o s s ω o s ω o s jω P σ P σ P ω
Types of Pole Transfer Functions (ont.) All Pass (Delay Equalizer) : ( Bandpass) ωo s H( s) s ω o s H ( ω ) s s ω o s ω o s Group Delay σ P jω P σ P APP0 State Variable Active Filter Lowpass & Bandpass : V BP Σ V LP APP ω ω State Variable Active Filter (ont.) APP State Variable Active Filter (ont.) APP3 ν ν F ν UT V BP Σ Σ s s V LP ν UT ν F ν F V LP s s s ω o s
V BP State Variable Active Filter (ont.) S ω o S S S S S (Note GAIN is at instead of as required for a canonical bandpass.) Highpass : Highpass ( Lowpass) ( Bandpass) Using a 3 D P AMP we form the sum, V HIGHPASS V LP V BP APP4 Bandstop : Bandstop ( Bandpass) V BANDSTP V BP All Pass : State Variable Active Filter (ont.) Allpass ( Bandpass) V ALLPASS V BP APP5 APP6 Active Filters Integrator or State Variable onfigurations Basic Element is the P AMP Integrator : ν IN i UT i in Virtual Ground ν UT APP7 Active Filters Integrator or State Variable onfigurations (ont.) i UT i in ν i in 0 in S iut ν UT ν in ν in 0 ν UT S νut S ν UT H( s) ν in S H( s) s jω jω
APP8 Active Filters Integrator or State Variable onfigurations (ont.) Scaling of the internal node voltages for maximum dynamic range. ν IN Σ ν n ν n ν UT APP9 Active Filters Integrator or State Variable onfigurations (ont.) For maximum dynamic range. (Signal / Noise atio) the outputs of both op amps should have the same peak values. If this is not true; If op amp # has a peak signal larger than #, then # will saturate early limiting the maximum signal. If # has a peak amplitude less than #, then there must be gain from # to # and the noise of # will be amplified. APP30 Basic Element of Switched apacitor Filters APP3 f ω 3kHz 0krad sec f c T V V V f c V 0pF 0pF 0 0 3 0 7 ( V V ) 5MΩ ± 0% ± 0% I f c ( V V ) T V V I f c ± 0%
Basic Element of Switched apacitor Filters (ont.) APP3 Size of Switched apacitor, esistors APP33 V UT f 3dB 0kHz 0pF π f 3dB.6M Ω ( 6.8) ( 0 4 ) ( 0 ) Area of S esistor ( f c 00kHz) f c 0 5.6 0 6 6.8pF 3mil s (@5mil pf ) Area of Poly esistor 3 0 3 ( 50Ω ) 3. 0 3 mil s (@mil ) Equivalent S resistor about orders of magnitude smaller in area. Simple Filter APP34 S Integrator APP35 V UT V UT 0pF α ω3db ω 3dB f c f c equires absolute control of and equires control of atios of
Two Integrators Together APP36 Time Switched Equivalent ircuit APP37 α V LP α V BP VIN APP38 APP39 ε Si0 t Acap Ω ( # ) Acap # 0.5 0 0.5
.4GHz F Front End APP40 800 900MHz rystal Frequency eference Digital adio Front End 50Ω Matched Impedance 50Ω A/D