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## Circuit Types and Analysis

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**Circuit Types and Analysis**• DFM = Design for Manufacturing • DFR = Design for Reliability**Linear Analog Circuit Blocks**• Amplifiers and Attenuators • Math Functions (add, subtract) • Oscillators (sinusoidal) • Filters • Voltage Regulators • Voltage References**Non-Linear Analog Circuit Blocks**• Comparators • Oscillators (non-sinusoidal, square, sawtooth, etc) • Voltage Limiters and Clamps • Rectifiers and Bridges • Math Functions (multiply, divide) • Log and other Non-linear Amplifiers • Sample and Hold Amplifiers • Envelope & Peak Detectors • Phase Detectors • Phased Locked Loops • Switching Voltage Regulators**Passive Components, R-L-C**• 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**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,**+**- • Amplifiers**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)**Basic Gain in Voltage, Current or CombinationLinear**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**+**- Operational AmplifierLinear, 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**+**- Operational AmplifierIdeal Assumptions Vp Used for basic analysis, nominal gain analysis Vout • 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 Vn**+**- Operational AmplifierPower Supplies Vcc Vp Power Supplies can be a critical consideration Vout • -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) Vn -Vcc**+**- Operational AmplifierBasic Applications Rf Av = - Rf/Ri Zin = Ri Inverting Voltage Amp Ri Vin Vout Rp**+**- Operational AmplifierBasic Applications Ri Av = 1 + Rf/Rp Zin = Ri + Non-Inverting Voltage Amp When Rf=0, Rp=~Infinite…… Av = 1 Vin Vout Rf Rp 8**+**- Operational AmplifierBasic Applications Av = 1 Zin = Unity Gain Voltage Amp Vin Vout 8**+**- Operational AmplifierBasic Applications Ri Gm = 1/Rp Zin = Ri + Transconductance Amp Vin RL Iout Rp 8**+**- Operational AmplifierBasic Applications Rf Zm = - Rf Transimpedance Amp Iin Vout RL**+**- Operational AmplifierBasic Applications Ai = -(1 + Ri/Rp) Current Amplifier Iin RL Ri Iout Rp**+**- Operational AmplifierIdeal Assumptions Vp Used for basic analysis, nominal gain analysis Vout • 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 Vn**+**- Operational AmplifierReal Characteristics Ip Vp Vout Used for more accurate Gain Characterization Iout Vio • Vout = Ad(Vp – Vn) + Ac(Vp + Vn)/2 + Vio Ad is the diff gain, Ac is the common mode gain, Vio = offset voltage • 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 In Vn**+**- Operational AmplifierReal Characteristic Effects Basic Strategy Vp • 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 Vout Vn**+**- Inverting ConfigurationOffset Error Contribution 1 Rf Ii = (0-Vio)/Ri If = (Vio-Vo)/Rf Ii = If Vo = Vio(1 + Rf/Ri) = Verr Inverting Voltage Amp Error Voltage due to Vio Ri If Vout Vio Ii Rp**+**- Non-inverting ConfigurationOffset Error Contribution 1 Ri 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 Vin Vout Vio Rf If Rp Ii**+**- Inverting AmplifierOffset Error Contribution 2 Rf 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)(Ib+/-Iio)] Note if Iio = ~0 and Rp = Rf//Ri, then Verr = 0 Verr is always minimized when Rp = ~Rf//Ri Inverting Voltage Amp Error Voltage due to Ib, Iio Ri If Vin Vout Iio Ii Ib Ib Rp**+**- Non-Inverting AmplifierOffset Error Contribution 2 Rf At V+: Iio = Ib + V+/Ri V+ = Ri(Iio-Ib) At V-: -V-/Rp = (V--Vout)Rf + Ib + Iio Sub V+ into above equation Vo = Verr = Rf(Ib-/+Iio) - [((RfRi)/Rp + Ri)(Ib+/-Iio)] Note if Iio = ~0 and Ri = Rf//Rp, then Verr = 0 Verr is always minimized when Ri = Rf//Rp Non-Inverting Voltage Amp Error Voltage due to Ib, Iio Rp If Vout Iio Ip Ib Ib Ri Ii Vin**+**- Inverting AmplifierGain 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% !**+**- Non-Inverting AmplifierGain 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% !**+**- Operational AmplifierGain 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**Total Error**• Verr due to Gain Error incl Resistor tolerance • Verr due to Offset and Bias Effects • Requirements may dictate an outright nominal gain plus a total error voltage or current budget**10K 5%**0.1V Vout 10K 1% + - 1K 1% Example • Find Overall Worst Case DC Error Voltage Nominal Gain = 1+Rf/Ri = +11.0 Nominal Output = 1.1V TLO72C**10K 5%**0.1V Vout 10K 1% + - 1K 1% Analysis requires opamp data sheet info TLO72C • TL072C over 0-70C: • Ib(max) = 7nA • Iio(max) = 2nA • Vio(max) = 13mV • Avo(min) = 15000**10K 5%**0.1V Vout 10K 1% + - 1K 1% Non-Inverting AmplifierGain Error Av (nom) = 1+ Rf/Rp = 11.0 Av (min) Rf down 1% 9.9KW, Rp up 1% 1.01KW Av = Ad(Rp + Rf)/(RpAd + Rp + Rf) Av = Av(nom)/CF CF = Correction Factor CF = 1 + 1/Ad + Rf/(RpAd) TLO72C Av(min) = 15K(1.01+9.9) / [(15K)(1.01) + 9.9 + 1.01] = 10.79 Error from nominal = 11.0 – 10.79 = 0.21 21mV Av(max) = 15K(0.99+10.1) / [(15K)(0.99) + 10.1 + 0.99] = 11.19 Error from nominal = 0.19 = |11.0 – 11.19| = 0.19 19mV Worst Case Gain Error assuming Vin = 0.1V = 19mV or 21mV**10K 5%**0.1V Vout 10K 1% + - 1K 1% Non-inverting ConfigurationOffset Error Contribution 1 Verr1 = Vio(1 + Rf/Rp) Verr1a(max) = 13mV(1 + 10.1/0.99) = 145.6mV Verr1b(max) = 13mV(1 + 9.9/1.01) = 140.4mV TLO72C Worst Case Offset 1 Error = 145.6mV or 140.4mV**10K 5%**0.1V Vout 10K 1% + - 1K 1% Non-Inverting AmplifierOffset Error Contribution 2 Verr2 = Rf(Ib-/+Iio) - [((RfRi)/Rp + Ri)(Ib+/-Iio)] Verr2 = 10(7nA-/+2nA) – [(10)(10)/1 + 10](7nA+/-2nA) Verr2 worst case = ~1mV TLO72C Worst Case Offset 2 Error = ~1mV**Total Error**• Verr due to Gain Error = 19.0mV • Verr due to Offset 1 = 145.6mV • Verr due to Offset 2 = 1mV Answer: Worst Case Total Error = 165.6mV (when Rf = max, Rp = min)**+**- Operational AmplifierGain vs Bandwidth Tradeoff Rf 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 140dB or higher • When Ad(f) = 1, f = Unity Gain Freq • Above fcl, Av will fall at 20db/dec (8db/oct) Ri Vin Vout Rp**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)**Filter Basics**• Linear Operation Must Be Maintained: • Gain is Frequency Dependent but …. • No New Frequencies are Created**Basic Low Pass Filter**Potential Filter Shapes**Basic High Pass Filter**Potential Filter Shapes**Basic BandPass Filter**Potential Filter Shapes**Basic BandStop Filter**Potential Filter Shapes**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