PHYS289 Lecture 4. Electronic Circuits

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1 PYS89 Lecture 4 Electronic ircuits

2 ourse Web Page Up no ontains All lecture notes PDF Useful links

3 Last lecture Waveforms, frequencies, etc. Often useful to think in Fourier space about the response of a circuit Many different kinds of useful signals Square ave Sinusoid Pulses ircuits ith capacitors hange the behavior of a circuit versus time Integrate, differentiate, delay change phase, etc. The R time constant haracteristic time of change Inductors and transformers

4 Transfer Functions out in The transfer function describes the behavior of a circuit at out for all possible in.

5 Simple Example 3 3 * R R R R R in out k k k k k in out 3 3 * 6 5 in out kt t then kt t if out in sin 5 sin 6

6 More omplicated Example What is no? no depends upon the input frequency = f because the capacitor and inductor make the voltages change ith the change in current.

7 o do e model? We ant a ay to combine the effect of the components in terms of their influence on the amplitude and the phase. Easier if the signals are sinusoids cycle in time derivatives and integrals are ust phase shifts and amplitude changes

8 Phasors A, A phasor is a function of the amplitude and phase of a sinusoidal signal Phasors allo us to manipulate sinusoids in terms of amplitude and phase changes. Phasors are based on complex polar coordinates. f Using phasors and complex numbers e ill be able to find transfer functions for circuits.

9 Revie of Polar oordinates point P is at r p cosɵ p, r p sinɵ p P tan y x P P r P x P y P

10 Revie of omplex Numbers z p is a single number represented by to numbers z p has a real part x p and an imaginary part y p

11 omplex Polar oordinates z = x+y here x is A cos and y is A sin t cycles once around the origin once for each cycle of the sinusoidal ave =f

12 No e can define Phasors if t Acos t, then let Acos t Asin t or simply, Acos Asin t is common to each term, so it is dropped. The real part is our signal. The to parts allo us to determine the influence of the phase and amplitude changes mathematically. After e manipulate the numbers, e discard the imaginary part.

13 The =IR of Phasors IZ The influence of each component is given by Z, its complex impedance Once e have Z, e can use phasors to analyze circuits in much the same ay that e analyze resistive circuits except e ill be using the complex polar representation.

14 Magnitude and Phase Acos x y tan y x Asin A x y magnitude phase of of Phasors have a magnitude and a phase derived from polar coordinates rules.

15 Influence of Resistor on ircuit R I R R if I R t Asin t then R t R * Asin t Resistor modifies the amplitude of the signal by R Resistor has no effect on the phase

16 Influence of Inductor on ircuit if I L then or t L L t L t di dt Inductor modifies the amplitude of the signal by L Inductor shifts the phase by +/ L L Asin t L* Acos t L* Asin t Note: cosq=sinq+p/

17 Influence of apacitor on ircuit apacitor modifies the amplitude of the signal by / apacitor shifts the phase by -/ dt I sin * sin * cos * cos * sin t A t A t or t A t A t then t A t I if

18 Understanding Phase x y tan 8 tan : 9 tan : 9 tan : tan : or x then x and y if real y then y and x if y then y and x if x then x and y if real

19 omplex Impedance IZ Z defines the influence of a component on the amplitude and phase of a circuit Resistors: Z R = R change the amplitude by R apacitors: Z =/ change the amplitude by / shift the phase -9 /=- Inductors: Z L =L change the amplitude by L shift the phase +9

20 omplex Impedance Z defines the influence of a component on the amplitude and phase of a circuit Resistors: Z R = R apacitors: Z =/ Inductors: Z L =L IZ We can use the rules for resistors to analyze circuits ith capacitors and inductors if e use phasors and complex impedance.

21 Simple Example R R Z Z Z I Z Z I Z R R in out Z R Z R

22 Simple Example continued R R R R tan tan tan R R R R tan R

23 R Frequency The corner frequency of an R or RL circuit tells us here it transitions from lo to high or visa versa. We define it as the place here For R circuits: For RL circuits: c c R R L c

24 orner Frequency of our example R R R R R c R

25 , c, and filters We can use the transfer function,, and the corner frequency, c, to easily determine the characteristics of a filter. If e consider the behavior of the transfer function as approaches and infinity and look for hen nears and, e can identify high and lo pass filters. The corner frequency gives us the point here the filter changes: c fc

26 Taking limits b b b a a a At lo frequencies, ie. = -3, loest poer of dominates At high frequencies ie. = +3, highest poer of dominates b a b b b a a a b a b b b a a a

27 Our example at lo frequencies R LOW LOW as LOW tan on x axis

28 Our example at high frequencies R IG IG IG as tan R R tan R

29 Our example is a lo pass filter LOW IG f c c R. What about the phase?.5.z z Kz.Mz Mz : / R: Frequency

30 igh pass filter an also make high pass filters Useful for removing D component of a signal

31 Equivalent Impedance Even though this filter has parallel components, e can still handle it. We can combine complex impedances like resistors to find the equivalent impedance of the components combined.

32 Equivalent Impedance L L L L L L Z Z Z Z Z L L L

33 Determine L L Z L L L R L L L by multiply L L R L L L L Z R Z

34 At ery Lo Frequencies R L LOW LOW LOW At ery igh Frequencies R LR L IG IG IG

35 At some Resonant Frequency L L L L R L L L

36 example of a band pass filter..5 d d R / :+ Magnitude = at = at = at Phase f = 9 at f = at SEL>> -d.z Kz Mz PR: f Frequency f = -9 at

37 an combine filters to tune the response Removes the need to use an inductor

38 omplex Impedance Z defines the influence of a component on the amplitude and phase of a circuit Resistors: Z R = R apacitors: Z =/ Inductors: Z L =L IZ We can use the rules for resistors to analyze circuits ith capacitors and inductors if e use phasors and complex impedance.

39 Diodes Most modern diodes are semiconductor devices, but are considered passive since they do not contribute any amplification or gain to a circuit. athode Anode

40 Diode types May be classified by semiconductor material silicon, germanium, gallium arsenide, etc. Or classified by circuit function Small signal detector or sitching diode Rectifier diode Light-emitting diode LED

41 Diode Ratings Peak inverse voltage PI Maximum forard current I F Maximum forard voltage drop F Reverse leakage current I R

42 Diodes Diodes are essentially one-ay current gates Symbolized by: urrent vs. voltage graphs: I I I I acts ust like a ire ill support arbitrary current provided that voltage is positive.6 plain resistor diode idealized diode WAY idealized diode no current flos current flos the direction the arro points in the diode symbol is the direction that current ill flo

43 Diode Makeup p-type n-type Diodes are made of semiconductors usually silicon Essentially a stack of p-doped and n-doped silicon to form a p-n unction doping means deliberate impurities that contribute extra electrons n-doped or holes for electrons p-doped Transistors are n-p-n or p-n-p arrangements of semiconductors

6 drop When electron flos through LED, loses energy by emitting a photon of light rather than vibrating

44 LEDs: Light-Emitting Diodes Main difference is material is more exotic than silicon used in ordinary diodes/transistors typically -volt drop instead of.6 drop When electron flos through LED, loses energy by emitting a photon of light rather than vibrating lattice heat LED efficiency is 3% compare to incandescent bulb at % Must supply current-limiting resistor in series: figure on drop across LED; aim for ma of current

Getting D back out of A A provides a means for us to distribute electrical poer, but most devices actually ant D bulbs, toasters, heaters, fans don t care: plug straight in sophisticated devices care

45 Getting D back out of A A provides a means for us to distribute electrical poer, but most devices actually ant D bulbs, toasters, heaters, fans don t care: plug straight in sophisticated devices care because they have diodes and transistors that require a certain polarity rather than oscillating polarity derived from A this is hy battery orientation matters in most electronics Use diodes to rectify A signal Simplest half-ave rectifier uses one diode: input voltage A source load diode only conducts hen input voltage is positive voltage seen by load

Doing Better: Full-ave Diode Bridge The diode in the rectifying circuit simply prevented the negative sing of voltage from conducting but this astes half the available cycle also

46 Doing Better: Full-ave Diode Bridge The diode in the rectifying circuit simply prevented the negative sing of voltage from conducting but this astes half the available cycle also very irregular bumpy: far from a good D source By using four diodes, you can recover the negative sing: B & conduct A source A B input voltage D load A & D conduct voltage seen by load

Full-Wave Dual-Supply By grounding the center tap, e have to opposite A sources the diode bridge no presents + and voltages relative to ground each can be

47 Full-Wave Dual-Supply By grounding the center tap, e have to opposite A sources the diode bridge no presents + and voltages relative to ground each can be separately smoothed/regulated cutting out diodes A and D makes a half-ave rectifier A source A B voltages seen by loads load D + load can buy pre-packaged diode bridges

Smoothing out the Bumps Still a bumpy ride,

during lo spots voltage regulator smoothes

48 Smoothing out the Bumps Still a bumpy ride, but e can smooth this out ith a capacitor capacitors have capacity for storing charge acts like a reservoir to supply current during lo spots voltage regulator smoothes out remaining ripple A source A B capacitor D load

49 o smooth is smooth? R An R circuit has a time constant = R because d/dt = I/, and I = /R d/dt = /R so is expt/ Any exponential function starts out ith slope = Amplitude/ So if you ant < % ripple over z 8.3 ms timescale must have = R > 83 ms if R =, > 83 F

50 Regulating the oltage The unregulated, ripply voltage may not be at the value you ant depends on transformer, etc. suppose you ant 5. You could use a voltage divider to set the voltage But it ould droop under load output impedance R R need to have very small R, R to make stiff the divider ill dra a lot of current R perhaps straining the source poer expended in divider >> poer in load Not a real solution Important note: a big load means a small resistor value: demands more current than M in R 3 out R load

51 The Zener Regulator Zener diodes break don at some reverse voltage can buy at specific breakdon voltages as long as some current goes through zener, it ll ork good for rough regulation onditions for orking: let s maintain some minimal current, I z through zener say a fe ma then in out /R = I z + out /R load sets the requirement on R because presumably all else is knon if load current increases too much, zener shuts off node drops belo breakdon and you ust have a voltage divider ith the load in R Z zener voltage high slope is hat makes the zener a decent voltage regulator out = z R load

52 oltage Regulator I an trim don ripply voltage to precise, rock-steady value No things get complicated! We are no in the realm of integrated circuits Is Is are hole circuits in small packages Is contain resistors, capacitors, diodes, transistors, etc. note zeners

53 oltage Regulators The most common voltage regulators are the LM78XX + voltages and LM79XX voltages XX represents the voltage 785 is +5; 795 is 5; 785 is +5, etc typically needs input > 3 volts above output reg. voltage beare that housing is not alays ground A versatile regulator is the LM37 + or LM output out =.5+R /R + I ad R Up to.5 A picture at right can go to 5 datasheetcatalog.com for details

PHYS225 Lecture 19. Electronic Circuits

PHYS225 Lecture 19. Electronic Circuits PHYS225 Lecture 19 Electronic Circuits Last lecture Oscillators and timers Useful for many applications Periodic signals Controls Simple RC decay coupled to a comparator can produce many useful oscillations