Real Number Models for Op Amp Filters Implemented in...
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Joint International Conference OPTIM-ACEMP Optimization of Electrical & Electronic Equipment Aegean Conference on Electrical Machines & Power Electronics May 25-27, 2017, Brasov Romania Real Number Models for Op Amp Filters Implemented in VHDL Adrian Virgil Cr ăciun, Siemens CT, Transilvania University; Brașov, Romania Corporate Technology Siemens SRL, Romania Real Number Modeling: • Models analog block operation as discrete real data; • It is a representation of analogue functionality in the digital world; • Digital simulation speeds permit high volume regression tests. This paper presents the functional simulation results based on an original model of the analog filters with op amps, compares the results with the pure analog SPICE simulation and analyzes the limits of the proposed model. The Op Amp parameters included in the model are: • the input offset voltage: V I0 – simply added to the input voltage; • the output saturation: V o_H and V o_L – high and low saturation voltages; • the slew rate limitation (max. output voltage variation with time): SR; • the finite open-loop voltage gain at dc: a v0 . b) a) R 1 R o v C v i + - R o v + - v i C 2 R V o_SR = V o_SR_H YES NO YES NO V o > V o_SR_H V o < V o_SR_L V o_SR = V o_SR_L V o_SR = V o V o_CLP = V o_H YES NO YES NO V o_SR > V o_H V o_SR < V o_L V o_CLP = V o_L V o_CLP = V o_SR V o_SR_L = V o,n-1 – SR x T s V o_SR_H = V o,n-1 + SR x T s The schematics of the low-pass / high-pass filters with op amps The Op Amp slew-rate and saturation limitations algorithm. 3. Conclusions This paper describes simple real number models of op amp low-pass and high-pass filters. The steps of op amp filters modeling presented in this paper are: 1. Derive the s-domain transfer function; 2. Use the bilinear transform to derive the z-domain function; 3. Solve the output as function of input and older values of input and output; 4. Implement the function in VHDL. The op amp model is completed with: input offset voltage, SR limitation, open-loop voltage gain at dc and saturation voltages. Comparison results of the simulation using SPICE and VHDL models, simulated in LTspice and ModelSim: • The behavior of both models is similar for sine input, square input, SR and saturation limitations with a precision of the output wave global parameters better than 0.8%; • The VHDL simulation does not contain some 2nd order effects: the glitches of fast slope variations and the smoothing of the output voltage slope variations produced by SR limitations. • The proposed model gives a good representation of the circuit behavior and has been successfully used with digital simulators. 2. SPICE Model versus RNM Model for the Op Amp Low - Pass Filter 1. The Real Number Model Development for the Op Amp Low - Pass Filter The z-domain transfer function for the op amp low-pass filter is: where: Solved for V o : In terms of input and delayed values of input and output: The previous formula can be used for any 1 st order s-domain function transferred in z-domain with bilinear transform: 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 z d d z n n z K K z A A z z K A V V z H v v v i o interval sampling , 1 , 1 , 2 2 , 1 0 2 2 2 0 1 0 s s s v T K d K d T C R T K R R A n n 0 1 1 1 1 0 ) ( d z d V z n n V V o i o 0 1 1 , 1 1 , 0 , d d V n V n V V n o n i n i o 1 1 1 1 2 z z T s s LTspice and VHDL simulations to verify the model SR limitation LTspice and VHDL simulations results for the op amp integrator LTspice and VHDL LTspice and VHDL simulations waveshaping circuit to verify the clipping and simulations LTspice and VHDL simulations for a nonlinear waveshaping The parameters for the VHDL Op Amp model were chosen to be close to the SPICE ones. ELECTRONICĂ și CALCULATOARE
Transcript of Real Number Models for Op Amp Filters Implemented in...
Joint International Conference OPTIM-ACEMP
Optimization of Electrical & Electronic Equipment
Aegean Conference on Electrical Machines & Power Electronics
May 25-27, 2017, Brasov Romania
Real Number Models for Op Amp Filters Implemented in VHDL
Adrian Virgil Crăciun,Siemens CT, Transilvania University; Brașov, Romania
Corporate Technology
Siemens SRL, Romania
Real Number Modeling:• Models analog block operation as discrete real data;• It is a representation of analogue functionality in the digital world;• Digital simulation speeds permit high volume regression tests.
This paper presents the functional simulation results based on an original model of the analog filters with op amps, compares the results with the pure analog SPICE simulation and analyzes the limits of the proposed model.
The Op Amp parameters included in the model are:• the input offset voltage: VI0 – simply added to the input voltage;• the output saturation: Vo_H and Vo_L – high and low saturation voltages;• the slew rate limitation (max. output voltage variation with time): SR;• the finite open-loop voltage gain at dc: av0.
b)a)
R
1R
ov
Cv i
+
-R
ov
+
-
v i C
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Vo_SR = Vo_SR_H
YES
NO
YES
NOVo > Vo_SR_H
Vo < Vo_SR_L
Vo_SR = Vo_SR_L
Vo_SR = Vo
Vo_CLP = Vo_H
YES
NO
YES
NOVo_SR > Vo_H
Vo_SR < Vo_L
Vo_CLP = Vo_L
Vo_CLP = Vo_SR
Vo_SR_L = Vo,n-1 – SR x Ts
Vo_SR_H = Vo,n-1 + SR x Ts
The schematics of the low-pass/ high-pass filters with op amps
The Op Amp slew-rate andsaturation limitations algorithm.
3. Conclusions
This paper describes simple real number models of op amp low-pass and high-pass filters.
The steps of op amp filters modeling presented in this paper are: 1. Derive the s-domain transfer function;
2. Use the bilinear transform to derive the z-domain function;
3. Solve the output as function of input and older values of input and output;
4. Implement the function in VHDL.
The op amp model is completed with: input offset voltage, SR limitation, open-loop voltage gain at dc and saturation voltages.
Comparison results of the simulation using SPICE and VHDL models, simulated in LTspice and ModelSim:• The behavior of both models is similar for sine input, square input, SR and
saturation limitations with a precision of the output wave global parameters better than 0.8%;
• The VHDL simulation does not contain some 2nd order effects: the glitches of fast slope variations and the smoothing of the output voltage slope variations produced by SR limitations.
• The proposed model gives a good representation of the circuit behavior and has been successfully used with digital simulators.
2. SPICE Model versus RNM Model for the Op Amp Low-Pass Filter
1. The Real Number Model Development for the Op Amp Low-Pass Filter
The z-domain transfer function for the op amp low-pass filter is:
where:
Solved for Vo:
In terms of input and delayed values of input and output:
The previous formula can be used for any 1st
order s-domain function transferred in z-domain with bilinear transform:
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LTspice and VHDL simulations to verify the model SR limitation
LTspice and VHDL simulationsresults for the op amp integrator
LTspice and VHDL LTspice and VHDL simulations waveshaping circuit to verify the clipping and simulations
LTspice and VHDL simulations for a nonlinear waveshaping
The parameters for the VHDL Op Amp model were chosen to be close to the SPICE ones.
ELECTRONICĂ și CALCULATOARE
