1. Circuit Types and Analysis
DFM = Design for Manufacturing

2. 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

3. 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,

4. Passive Component Specifications

5. 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)

6. 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

7. 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

8. Basic Op-Amp Simplified Implementation

9. 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

10. 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)

11. Operational Amplifier Classifications

12. Operational Amplifier Basic ApplicationsRf Ri - +
Vin
Vout
Av = - Rf/Ri
Zin = Ri
Inverting Voltage Amp Rp

13. Operational Amplifier Basic ApplicationsRi + -
Vin
Vout Rf
Av = 1 + Rf/Rp
Zin = Ri +
Non-Inverting Voltage Amp
When Rf=0, Rp=~Infinite…… Av = 1 Rp 8

14. Operational Amplifier Basic Applications+ -
Vin
Vout
Av = 1
Zin =
Unity Gain Voltage Amp 8

15. Operational Amplifier Basic ApplicationsRi + -
Vin RL
Iout Rp
Gm = 1/Rp
Zin = Ri +
Transconductance Amp 8

16. Operational Amplifier Basic ApplicationsRf - +
Iin
Vout RL
Zm = - Rf
Transimpedance Amp

17. Operational Amplifier Basic Applications+ -
Iin RL Ri
Iout Rp
Ai = -(1 + Ri/Rp)
Current Amplifier

18. Operational Amplifier Real CharacteristicsIp + - 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

19. 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

20. Inverting Configuration Offset Error Contribution 1Rf 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

21. 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

22. Op-Amp Technologies (EDN) Offset Voltage ComparisonsIO

23. Op-Amp Technologies (EDN) Input Bias Current
10 deg C

24. Operational Amplifier Offset Error Contribution 2Rf 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

25. Inverting Amplifier Gain ErrorRf
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% !

26. Non-Inverting Amplifier Gain ErrorRi + -
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% !

27. Operational Amplifier Gain ErrorRf 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

28. 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

29. Operational Amplifier Gain vs Bandwidth TradeoffRf - + 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)

30. Common Sensor Interface Requirements (EDN)

31. 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)

32. Linear Operation Must Be Maintained:
Filter Basics
Linear Operation Must Be Maintained:
Gain is Frequency Dependent but ….
No New Frequencies are Created

33. Potential Filter Shapes
Basic Low Pass Filter
Potential Filter Shapes

34. Potential Filter Shapes
Basic High Pass Filter
Potential Filter Shapes

35. Potential Filter Shapes
Basic BandPass Filter
Potential Filter Shapes

36. Potential Filter Shapes
Basic BandStop Filter
Potential Filter Shapes

37. 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

38. Effect of Shape Factor on Filters
Lowpass
Highpass
Bandpass
Bandstop

39. 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

40. Basic 2nd Order Implementations - Hambley
Lowpass
Highpass
Bandpass

41. 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:

43. 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

44. 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)

45. 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)

46. Wein Bridge Oscillator
Loop Gain

47. 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

48. Analog Circuit DFM Analysis

49. Wien-Bridge Oscillator Example
Joe Student

50. 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.

51. Open Loop Analysis Z1 Z2

52. Analysis
The loop gain can be found by doing a voltage division Z1 Z2

53. Analysis
Assume the two RC Networks have equal R & C values Z1 Z2

54. Analysis Need to find the Gain over the whole Circuit: Vo/Vs
Solve G equation for V1 and substitute in for above equ.

55. Analysis We now have an equation for the overall circuit gain
Simplifying and substituting jw for s

56. 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

57. 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

58. Ideal vs. Non-Ideal Op-Amp
Red is the ideal op-amp.
Green is the 741 op-amp.

59. Making the Oscillations Steady
Add a diode network to keep circuit around G = 3
If G = 3, diodes are off

60. 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.

61. Making the Oscillations Steady
When output voltage is negative, D2 turns on and R9 is switched in parallel causing G to drop

62. Results of Diode Network
With the use of diodes, the non-ideal op-amp can produce steady oscillations.

63. Frequency Analysis
By changing the resistor and capacitor values in the positive feedback network, the output frequency can be changed.

64. Frequency Analysis
Fast Fourier Transform of Simulation