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ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE.

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Presentation on theme: "ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE."— Presentation transcript:

1 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Registered Electrical & Mechanical Engineer Engineering 43 Diodes-2

2 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 2 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Learning Goals  Understand the Basic Physics of Semiconductor PN Junctions which form most Diode Devices  Sketch the IV Characteristics of Typical PN Junction Diodes  Use the Graphical LOAD-LINE method to determine the “Operating Point” of Nonlinear (includes Diodes) Circuits

3 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 3 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Learning Goals  Analyze diode-containing Voltage- Regulation Circuits  Use various math models for Diode operation to solve for Diode-containing Circuit Voltages and/or Currents  Learn The difference between LARGE-signal and SMALL-Signal Circuit Models IDEAL and PieceWise-Linear Models

4 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 4 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Diode Models  LoadLine Analysis works well when the ckt connected to a SINGLE Diode can be “Thevenized”  However, for NONLinear ckts, such as those containing multiple diodes, construction of the LOAD-Curve Eqn may be difficult, or even impossible.  Many such ckts can be analyzed by Idealizing the diode

5 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 5 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Diode Models  Consider an Electrical Diode →  We can MODEL the V-I Behavior of this Device in Several ways V I REAL Behavior IDEAL Model OFFSET Model LINEAR Model

6 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 6 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Ideal Model (Ideal Rectifier)  Analyze Ckts containing Ideal Diodes 1.Assume (or Guess) a “state” for each diode. Ideal Diodes have Two states 1.ON → a SHORT Ckt when Fwd Biased 2.OFF →an OPEN Ckt if Reverse Biased 2.Check the Assumed Opens & Shorts Should have Current thru the SHORTS Should have ∆V across the OPENS Diode ON Diode OFF

7 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 7 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Ideal Model (Ideal Rectifier) 3.Check to see if guesses for i-flow, ∆V, and BIAS-State are consistent with the Ideal-Diode Model 4.If i-flow, ∆V, and bias-V are consistent with the ideal model, then We’re DONE. If we arrive at even a SINGLE Inconsistency, then START OVER at step-1 Diode ON Diode OFF

8 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 8 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Ideal Diode  Find For Ckt Below find: Use the Ideal Diode Model

9 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 9 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Ideal Diode  Assume BOTH Diodes are ON or Conducting  In this Case V D1 = V D2 = 0  Thus D2 Anode is connected to GND  Then Find by Ohm  Next use KCL at Node-A (in = out)

10 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 10 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Ideal Diode  Using I D2 = 1 mA  Thus  Now must Check that both Diodes are indeed conducting  From the analysis  Thus the current thru both Diodes is positive which is consistent with the assumption 

11 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 11 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Ideal Diode  Since both Diodes conduct the Top of Vo is connected to GND thru D2 & D1  Another way to think about this is that since V D2 = 0 and V D1 = 0 (by Short Assumption) Find Vo = GND+V D2 +V D1 = GND = 0  Thus the Answer

12 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 12 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Ideal Diode  Find For Ckt Below find: Use the Ideal Diode Model Note the different values on R1 & R2 –Swapped

13 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 13 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Ideal Diode  Again Assume BOTH Diodes are ON, or Conducting  As Before V D1 = V D2 = 0  Again V B shorted to GND thru D1  Then Find by Ohm  Now use KCL at Node-B (in = out)

14 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 14 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Ideal Diode  Using I D2 = 1.01 mA  Thus  Now must Check that both Diodes are indeed conducting  From the analysis  We find and INCONSISTENCY and our Assumption is WRONG 

15 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 15 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Ideal Diode  Must Iterate  Assume D1 → OFF D2 → ON  In this Case D1 is an OPEN → I D1 =0  Current I D2 must flow thru BOTH Resistors  Then Find by Ohm

16 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 16 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Ideal Diode  Must Check that D1 is REVERSE Biased as it is assumed OFF  By KVL & Ohm  Thus D1 is INDEED Reverse-Biased, Thus the Ckt operation is Consistent with our Assumption 

17 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 17 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example  Ideal Diode  Calculate Vo by noting that:  D2 is ON → V D2 = 0 D1 is OFF → Current can only flow thru D2  In this case Vo = V B  By the Previous Calculation, Find

18 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 18 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Offset & Linear Models  The Offset Model  Better than Ideal, but no account of Forward-Slope  The Linear Model  The model eqn:  Yet more accurate, but also does not account for Rev-Bias Brk-Down

19 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 19 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Point Slope Line Eqn  When constructing multipiece-wise linear models, the Point-Slope Equation is extremely Useful Where –(x 1, y 1 ) & (x 2, y 2 ) are KNOWN Points  Example: Find Eqn for line-segment: (3,17) (19,5)

20 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 20 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Point Slope Line Eqn  Using the 2 nd Point  Can easily convert to y = mx+b  Multiply by m, move −5 to other side of = (3,17) (19,5)

21 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 21 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Slopes on vi Curve  With Reference to the Point-Slope eqn v takes over for x, and i takes over for y  The Slope on a vi Curve is a conductance  If the curve is NONlinear then the local conductance is the first Derivative  Recall the Op-Pt is also the Q-Pt

22 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 22 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Slopes on vi Curve  Finally recall that conductance & resistance are Inverses  Example: Find the RESISTANCE of the device associated with the VI curve that follows

23 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 23 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Slopes on vi Curve  Since R = 1/G Find the Device Resistance as  For a NONlinear vi curve the local slope then: r = 1/g  The General Reln

24 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 24 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example PieceWise Linear Model  Construct a PieceWise Linear Model for the Zener vi curve shown at Right

25 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 25 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis PieceWise Linear Zener  m for Segment A  Us Pt-Slp eqn with (0.6V,0mA) for Pt-1  Segment- B is easy

26 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 26 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis PieceWise Linear Zener  m for Segment C  Us Pt-Slp eqn with (−6V,0mA) for Pt-1  Thus the PieceWise Model for the Zener

27 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 27 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example PieceWise Linear Model  Alternatively in terms of Resistances  ADVICE: remember the Pt-Slope Line-Eqn

28 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 28 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Half-Wave Rectifier Ckt  Consider an Sinusoidal V-Source, such as an AC socket in your house, supplying power to a Load thru a Diode Power InputLoad Voltage

29 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 29 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis HalfWave Rectifier  Note that the Doide is FWD-Biased during only the POSITIVE half-cycle of the Source  Using this simple ckt provides to the load ONLY positive-V; a good thing sometimes  However, the positive voltage comes in nasty PULSES which are not well tolerated by positive-V needing loads

30 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 30 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Smoothed HalfWave Rectifier  Adding a Cap to the Circuit creates a Smoothing effect  In this case the Diode Conducts ONLY when v s >v C and v C =v L  This produces v L (t) and i L (t) curves  Note that i L (t) is approx. constant

31 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 31 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Smoothed HalfWave Rectifier  The change in Voltage across the Cap is called “Ripple”  Often times the load has a Ripple “Limit” from which we determine Cap size  From the i L (t) curve on the previous slide note: Cap Discharges for Almost the ENTIRE Cycle time, T (diode Off) The Load Current is approx. constant, I L  Recall from EARLY in the Class Ripple

32 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 32 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Smoothed HalfWave Rectifier  Also from Cap Physics (chp3)  In the Smoother Ckt the Cap charges during the “Ripple” portion of the curve  Equating the Charge & Discharge “Q’s find  Note that both these equations are Approximate, but they are still useful for initial Ckt Design  Solving the equations for the Cap Value needed for a given V r ChargeDischarge

33 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 33 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Smoothed HalfWave Rectifier  Find the Approximate Average Load Voltage V L,hi V L,lo

34 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 34 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Capacitor-Size Effect  Any load will discharge the capacitor. In this case, the output will depend on how the RC time constant compares with the period of the input signal.  The plots at right consider the various cases for the simple circuit above with a 1kHz, 5V sinusoidal input

35 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 35 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Full Wave Rectifier  The half-wave ckt will take an AC- Voltage and convert it to DC, but the rectified signal has gaps in it.  The gaps can be eliminated thru the use of a Full-Wave rectifier ckt  The Diodes are Face-to-Face (right) Butt-to-Butt (left)  This rectified output has NO Gaps

36 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 36 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Full Wave Rectifier Operation D1 Supplies V to Load D4 Supplies V to Load

37 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 37 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Full Wave Rectifier Smoothing  The Ripple on the FULL wave Ckt is about 50% of that for the half-wave ckt  Since the Cap DIScharges only a half-period compared to the half-wave ckt, the size of the “smoothing” cap is then also halved:

38 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 38 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Small Signal Models  Often we use NonLinear Circuits to Amplify, or otherwise modify, non-steady Signals such as ac-sinusoids that are small compared to the DC Operating Point, or Q-Point of the Circuit.  Over a small v or i range even NonLinear devices appear linear. This allows us to construct a so-called small signal Linear Model

39 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 39 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Small Signal Analysis  Small signal Analysis is usually done in Two Parts: 1.Large-Signal DC Operating Point (Q-Pt) 2.Linearize about the Q-Pt using calculus  Recall from Calculus  This approximation become more accrate as ∆y & ∆x become smaller

40 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 40 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Small Signal Analsyis  Now let y→i D, and x→ v D  Use a DC power Supply to set the operating point on the diode curve as shown at right This could be done using LoadLine methods  From Calculus  Next Take derivative about the Q-Pt

41 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 41 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Small Signal Analysis  About Q-Pt  Now if we have a math model for the vi curve, and we inject ON TOP of V DQ a small signal, ∆v D find  The derivative is the diode small-signal Conductance at Q

42 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 42 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Small Signal Analysis  In the large signal Case: R = 1/G  By analogy In the small signal case:  r = 1/g  Also since small signal analysis is associated with small amounts that change with time…  Define the Diode’s DYNAMIC, small- signal Conductance and Resistance

43 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 43 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Small Signal Analysis  Note Units for r d  Recall the approximation for i D  Change Notation for Small Signal conditions  Find r d for a “Shockley” Diode in majority FWD-Bias  Recall Shockley Eqn  Then the Large- signal Operating Point at v D = V DQ

44 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 44 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Small Signal Analysis  Taking the derivative of the Shockely Eqn  Recall from last sld  Sub this Reln into the Derivative Eqn  Recall  Subbing for di D /dv D

45 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 45 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Notation: Large, Small, Total  V DQ and I DQ are the LARGE Signal operating point (Q-Pt) DC quantities These are STEADY-STATE values  v D and i D are the TOTAL and INSTANTANEQOUS quantities These values are not necessarily steady- state. To emphasize this we can write v D (t) and i D (t)

46 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 46 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Notation: Large, Small, Total  v d and i d are the SMALL, AC quantities These values are not necessarily steady- state. To emphasize this we can write v d (t) and i d (t)  An Example for Diode Current notation

47 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 47 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Effect of Q-Pt Location  From Analysis

48 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 48 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis DC Srcs  SHORTS in Small-Signal  In the small-signal equivalent circuit DC voltage-sources are represented by SHORT CIRUITS; since their voltage is CONSTANT, they exhibit ZERO INCREMENTAL, or SIGNAL, voltage  Alternative Statement: Since a DC Voltage source has an ac component of current, but NO ac VOLTAGE, the DC Voltage Source is equivalent to a SHORT circuit for ac signals

49 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 49 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Setting Q, Injecting v  Consider this ckt with AC & DC V-srcs Sets Q Sets v d

50 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 50 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Large and Small Signal Ckts  Recall from Chps 3 and 5 for Caps: OPENS to DC SHORTS to fast AC  Thus if C 1 is LARGE it COUPLES v in (t) with the rest of the ckt  Similarly, Large C 2 couples to the Load  To Find the Q-point DEcouple v in and v o to arrive at the DC circuit

51 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 51 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Large and Small Signal Ckts  Finding the Large signal Model was easy; the Caps acts as an OPENS  The Small Signal Ckt needs more work Any DC V-Supply is a SHORT to GND The Diode is replaced by r d (or g d ) The Caps are Shorts  Thus the Small Signal ckt for the above

52 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 52 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: Small Signal Gain  Find the Small Signal Amplification (Gain), A v, of the previous circuit  Using the Small Signal Circuit  Note that R C, r d, and R L are in Parallel  And v o (t) appears across this parallel combination  The equivalent ckt

53 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 53 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Example: Small Signal Gain  Thus for this Ckt the Large, Small, and small-Equivalent ckts  Then the Amplification (Gain) by Voltage Divider

54 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 54 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis All Done for Today Small Signal BJT Amp  Common Collector Amplifier LARGE Signal Model SMALL Signal Model

55 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 55 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce Mayer, PE Registered Electrical & Mechanical Engineer Engineering 43 Appendix

56 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 56 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

57 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 57 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Small Signal Analysis  In the large signal Case: R = 1/G  By analogy In the small signal case:  r = 1/g  Also since small signal analysis is associated with small amounts that change with time…  Define the Diode’s DYNAMIC Conductance and Resistance

58 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 58 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis P10.67  Graph v o vs. v i for v i : −5V to +5V

59 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 59 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

60 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 60 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

61 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 61 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

62 ENGR-43_Lec-10b_Diode-2_SmallSignalAnalysis.pptx 62 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis


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