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Circuit Types and Analysis
DFM = Design for Manufacturing
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Passive Components, RLC
Critical Factors: Ambient Temperature Thermal Deratings & Variation of Primary Parameter (Temp Co) Maximum Imposed Voltage and/or Current Maximum Imposed dV/dT and/or Frequency Inductive Frequency (high frequency model) Minimum Analysis & Selection Considerations: Primary Parameter Tolerances (R, L, C %) Total Power vs Package Dissipation Maximum Voltage Composition, Specific die-electrics, construction, etc
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Passive Discretes Resistors/Inductors: Must specify or account for Tolerance, Power, Package and Temp Coefficient Derating Guide: ~50% of rated power or current Std Tolerances: 0.1%, 1%, 5%, 10% and 20% Constructional Anomalies: Max Voltage, Inductive with High Freq Capacitors: Must specify or account for Tolerance, WV, Polarization, Dielectric, Temp Co and Package Derating Guide: ~50% of rated voltage Std Tolerances: 1%, 2%, 5%, 10%, 20%, 80% Constructional Anomalies: Charge Leakage, Inductive with High Freq,
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Passive Component Specifications
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Small Signal Amplifiers
Critical Factors: Component Tolerances, particularly gain setting R’s OpAmp Input Offset Voltage (Vio), worse for high gain Input Bias Current (Ib), Input Offset Current (Iio) Finite Diff Gain (Ad) & Variation of Ad with Frequency Output Slew Rate and Output Vp-p at Maximum Frequency Worst Case Analysis: Total DC Offset error in Volts (1,2,3) Total Gain Error vs Nominal, Converted to Volts (1,4) Power Bandwidth for Application (1,5)
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Additional Parameters
Basic Gain in Voltage, Current or Combination Linear Operation: No New Frequencies Created Voltage Amplifiers (Vin >> Vout): Av = Vout/Vin Current Amplifiers (Iin >> Iout): Ai = Iout/Iin Transimpedance (Iin >> Vout): Zm = Vout/Iin Transconductance (Vin >> Iout): Gm = Iout/Vin Additional Parameters Input Impedance: Zin = Vin/Iin Output Impedance: Zout = {Vout(NL) – Vout(L)}/Iout Slew Rate (SR): Min dVout/dT Slew Rate BW = SR/2pVp where Vp = Peak Voltage
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Operational Amplifier Linear, Differential, High Gain Amplifier
+ - Advantages Over Single Ended Amplifier Block ?? Easy to add positive and negative feedback with differential input Single Ended Application Gains can be tightly controlled with external components and made insensitive to internal transistor gain variations Inherent noise rejection when noise enters both input terminals
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Basic Op-Amp Simplified Implementation
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Operational Amplifier Ideal Assumptions
+ - Vp Used for basic analysis, nominal gain analysis Vout Vn Vout = Ad (Vp – Vn) where Ad is the diff gain Ad = Infinite Zin = Infinite, Iin = 0 where Iin is the input current Vp = Vn because of infinite Ad, Vo may be non-zero under this condition Iout = Infinite (Often a false assumption) These basic assumptions allow simple circuit analysis to determine Nominal gain applications
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Operational Amplifier Power Supplies
Vcc + - Vp Power Supplies can be a critical consideration Vout Vn -Vcc -Vcc < Vout < Vcc At all times, Vout(max) may be as low as 2 to 5 volts below Vcc depending upon model Vcc, -Vcc sometimes referred to as “Rails” due to power distribution on some boards resembling tracks Many applications use “Split” supply Operation Split Supply means Vcc = |-Vcc| Some models characterized for 1 supply operation (but ALL will work there) Single Supply means –Vcc = 0 Vcc, -Vcc power pins should always be capacitively filtered with 0.1uf (usually ceramic monolithic X7R or similar)
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Operational Amplifier Classifications
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Operational Amplifier Basic Applications
Rf Ri - + Vin Vout Av = - Rf/Ri Zin = Ri Inverting Voltage Amp Rp
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Operational Amplifier Basic Applications
Ri + - Vin Vout Rf Av = 1 + Rf/Rp Zin = Ri + Non-Inverting Voltage Amp When Rf=0, Rp=~Infinite…… Av = 1 Rp 8
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Operational Amplifier Basic Applications
+ - Vin Vout Av = 1 Zin = Unity Gain Voltage Amp 8
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Operational Amplifier Basic Applications
Ri + - Vin RL Iout Rp Gm = 1/Rp Zin = Ri + Transconductance Amp 8
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Operational Amplifier Basic Applications
Rf - + Iin Vout RL Zm = - Rf Transimpedance Amp
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Operational Amplifier Basic Applications
+ - Iin RL Ri Iout Rp Ai = -(1 + Ri/Rp) Current Amplifier
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Operational Amplifier Real Characteristics
Ip + - Vp Vout Used for more accurate Gain Characterization Iout Vio In Vn Vout = Ad(Vp – Vn) + Ac(Vp + Vn)/2 + Vio Ad is the diff gain, Ac is the common mode gain, Vio = offset CMRR = Common Mode Rejection Ratio = 20log(Ad/Ac) Ib = Bias Current (Ave Current = [Ip + In]/2) Iio = Offset Current (Diff Current = Ip – In) Iout = Finite, Split between gain set components and load Vio = Input Diff Voltage reflected back from Vo under the condition the Vp = Vn = 0 Use superposition to understand contributions
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Operational Amplifier Real Characteristic Effects
+ - Basic Strategy Vp Vout Vn Consider the Effect Separately, then combine results Show Ib and Iio as input current sources Show Vio as diff voltage on Vp-Vn Use amended opamp in std application circuit, Vin=0 (grounded). Find Vout, all Vout will be Verror due to Offset and Bias
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Inverting Configuration Offset Error Contribution 1
Rf Ri If - + Vout Vio Ii Ii = (0-Vio)/Ri If = (Vio-Vo)/Rf Ii = If Vo = Vio(1 + Rf/Ri) = Verr Inverting Voltage Amp Error Voltage due to Vio Rp
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Non-inverting Configuration Offset Error Contribution 1
+ - Vin Vout Vio Rf Ii = (0-Vio)/Rp If = (Vio-Vo)/Rf Ii = If Vo = Vio(1 + Rf/Rp) = Verr Non-Inverting Voltage Amp Error Voltage due to Vio If Rp Ii
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Op-Amp Technologies (EDN) Offset Voltage Comparisons
IO
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Op-Amp Technologies (EDN) Input Bias Current
10 deg C
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Operational Amplifier Offset Error Contribution 2
Rf Ri If - + Vout Iio Ii Ib At V+: Iio = Ib + V+/Rp V+ = Rp(Iio-Ib) At V-: -V-/Ri = (V—Vout)Rf + Ib + Iio Sub V+ into above equation Vo = Verr = Rf(Ib+/-Iio)+/-[(RfRp/Ri +Rp)(Iio-/+Ib)] Note if Iio = ~0 and Rp = Rf//Ri, then Verr = 0 Verr is minimized when Rp = Rf//Ri Inverting Voltage Amp Error Voltage due to Ib, Iio Ib Rp
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Inverting Amplifier Gain Error
Rf Av (nom) = - Rf/Ri But Assume Vout = Ad(V+ - V-) Find expressions for V+ & V- Substitute into above Vout Solve for Vout/Vin = Av Av = -(RfAd)/(RiAd + Ri + Rf) Av = Av(nom)/CF CF = Correction Factor CF = 1 + 1/Ad + Rf/(RiAd) |Av| < |Av (nom)| Inverting Voltage Amp Ri If - + Vin Vout Ii Rp Don’t Forget to Factor in RTol% !
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Non-Inverting Amplifier Gain Error
Ri + - Vin Vout Av (nom) = 1+ Rf/Rp But Assume Vout = Ad(V+ - V-) Find expressions for V+ & V- Substitute into above Vout Solve for Vout/Vin = Av Av = Ad(Rp + Rf)/(RpAd + Rp + Rf) Av = Av(nom)/CF CF = Correction Factor CF = 1 + 1/Ad + Rf/(RpAd) |Av| < |Av (nom)| Non-Inverting Voltage Amp Rf Rp Don’t Forget to Factor in RTol% !
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Operational Amplifier Gain Error
Rf Ri If - + Vin Vout Ii Largest Error will be due to Rtol !! Gain Error = Av(nom) – Av Verr from Gain Error Verr = Vin(max) * Gain Error Rp
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Total Error Verr due to Offset and Bias Effects
Plus Verr due to Gain Error Requirements may dictate an outright nominal gain plus a total error voltage or current budget
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Operational Amplifier Gain vs Bandwidth Tradeoff
Rf - + Ri Vin Vout Rp Av = - Rf/Ri = Nominal Closed Loop Gain Ad (Op-amp) = Open Loop Gain Ad rolls off with frequency, 20db/dec, after first pole (~ 1 to 100 Hz) Bandwidth of Closed Loop Gain, Fcl, limited by Ad(f) Av <= Ad (fcl) Ad(0) = Typically 60dB to 140 dB or higher When Ad(f) = 1, f = Unity Gain Freq Above fcl, Av will fall at 20db/dec (8db/oct)
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Common Sensor Interface Requirements (EDN)
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Filters Critical Factors: Passive Component Tolerances
OpAmp Input Offset Voltage (Vio), worse for high gain Input Bias Current (Ib), Input Offset Current (Iio) Loading effects of input source, output loads Output Slew Rate and Output Vp-p at Maximum Frequency Worst Case Analysis: Transfer Function Analysis Total DC Offset error in Volts (1,2,3) Mag (dB) & Phase (deg) vs Frequency Plots (1,4) Power Bandwidth for Application (1,5) Pulse Response (topology, 4)
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Linear Operation Must Be Maintained:
Filter Basics Linear Operation Must Be Maintained: Gain is Frequency Dependent but …. No New Frequencies are Created
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Potential Filter Shapes
Basic Low Pass Filter Potential Filter Shapes
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Potential Filter Shapes
Basic High Pass Filter Potential Filter Shapes
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Potential Filter Shapes
Basic BandPass Filter Potential Filter Shapes
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Potential Filter Shapes
Basic BandStop Filter Potential Filter Shapes
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Filter Passband Shaping: Q = Quality (Shape) Factor For Filter
Filter Basics General 2nd Order Transfer Function where; Filter Passband Shaping: Q = Quality (Shape) Factor For Filter Q is related to the damping factor Q = 1/2a Put Xfer Function into form with D(s) above Find expression for Wo, then find Q or a
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Effect of Shape Factor on Filters
Lowpass Highpass Bandpass Bandstop
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To rescale, replace S with S/Wo(new)
Filter Scaling Filter Scaling: All filter coefficients and polynomials are normalized to Wo = 1 rad/sec To rescale, replace S with S/Wo(new) Given an RC implementation circuit, Wo may also be moved by rescaling the Capacitors
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Basic 2nd Order Implementations - Hambley
Lowpass Highpass Bandpass
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Multi-Function Filter Design
Summing Inv Amp Vout BP Vin -1 R1 C1 - + R2 C2 -1 + - + A1 -1 Vout HP A2 Vout LP Rp Rp Inv Amp -B See:
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Filter Simulation of Component Tolerances
Worst Case Analysis: Transfer Function Analysis Total DC Offset error in Volts Mag (dB) & Phase (deg) vs Frequency Plots Power Bandwidth for Application Pulse Response
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Comparators Critical Factors:
Passive Component Tolerances, Diode Clamp Tolerances Input Offset Voltage (Vio) Input Bias Current (Ib), Input Offset Current (Iio) Voh, Vol clamping voltages Output Slew Rate and Delay Vref Tolerance Worst Case Analysis: Vutp and Vltp (upper and lower trip points, 1,2,3,4,6) Total hysteresis voltage (1-4,6) Max switching frequency (5)
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Oscillators Critical Factors: Passive Component Tolerances
Loading effects of output loads Output Slew Rate and Output Vp-p at Frequency of Oscillation Worst Case Analysis: Transfer Function Analysis of any Linear Feedback Circuit Forward path gain Analysis at 0 or 180 deg phase response Mag (dB) & Phase (deg) Margins vs Frequency Plots (1,2) Variation of Fo (1,2) Power Bandwidth (3)
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Wein Bridge Oscillator
Loop Gain
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Voltage Regulators, Power Supplies
Critical Factors: Passive Component Tolerances (voltage set resistors) Loading effects Input voltage DC, AC and noise levels Filtration Capacitors Ambient Temperature Worst Case Analysis: DC Output voltage variation (1,2,3) AC Output ripple, noise (2,3,4) Critical device power dissipation, Junction Temp (2,3,5) Startup Output voltage vs Input voltage vs Time (2,3,4) Safety Considerations
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Analog Circuit DFM Analysis
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Wien-Bridge Oscillator Example
Joe Student
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Wien-Bridge Theory of Operation
Uses phase shift RC networks connected to a forward path NI Amp Amplifier-Feedback Loop Gain = 1 Loop Phase = 0o The Wien-bridge oscillator is a unique circuit because it generates an oscillatory output signal without having a sinusoidal input source. Instead, it uses capacitors with initial voltages to create the output. This circuit can be especially useful if connected to a voltage follower to de-couple the load from the source. As you can see, the Wien-bridge oscillator uses two RC networks connected to the positive terminal to form a frequency selective feedback network. It also amplifies the signal with the two negative feedback resistors.
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Open Loop Analysis Z1 Z2
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Analysis The loop gain can be found by doing a voltage division Z1 Z2
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Analysis Assume the two RC Networks have equal R & C values Z1 Z2
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Analysis Need to find the Gain over the whole Circuit: Vo/Vs
Solve G equation for V1 and substitute in for above equ.
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Analysis We now have an equation for the overall circuit gain
Simplifying and substituting jw for s
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Analysis If G = 3, oscillations occur
If the negative feedback resistors are set so G = 3, then T(jw) = 1 and oscillations will occur. If G is less than three then oscillations attenuate. If G greater than 3 then oscillations amplify. If G = 3, oscillations occur If G < 3, oscillations attenuate If G > 3, oscillation amplify
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G = 3 G = 2.9 In order to keep the oscillations constant, Hewlett Packard put a lamp in the circuit at R1. The resistance of the lamp is strongly dependent on the temperature of the filament of the bulb. If the amplitude is too high, the current becomes large and the resistance of the lamp increases, thereby reducing the gain. If the amplitude is low, the lamp cools, the resistance decreases, and the loop gain increases. Using a lamp, however, is not practical so we use diodes. The book has a few different ways to hook up diodes to the circuit. I looked at the following circuit which is not in the book. G = 3.05
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Ideal vs. Non-Ideal Op-Amp
Red is the ideal op-amp. Green is the 741 op-amp.
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Making the Oscillations Steady
Add a diode network to keep circuit around G = 3 If G = 3, diodes are off
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Making the Oscillations Steady
When output voltage is positive, D1 turns on and R9 is switched in parallel causing G to drop G must be set a little higher than 3 with the diode configuration so that the diodes will work properly.
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Making the Oscillations Steady
When output voltage is negative, D2 turns on and R9 is switched in parallel causing G to drop
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Results of Diode Network
With the use of diodes, the non-ideal op-amp can produce steady oscillations.
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Frequency Analysis By changing the resistor and capacitor values in the positive feedback network, the output frequency can be changed.
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Frequency Analysis Fast Fourier Transform of Simulation
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