examples of fundamental importance (mostly resistive circuits)
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set out basic relations look at a few examples of fundamental importance (mostly resistive circuits) look at diodes, voltage regulation, transistors discuss impedances (cable, output, etc.)
examples of fundamental importance (mostly resistive circuits)
- 2. 2 Basic Circuit Analysis Basic Circuit Analysis • What we won’t do: What we won’t do: – common electronics-class things: RLC, filters, detailed analysis • What we will do: What we will do: – set out basic relations – look at a few examples of fundamental importance (mostly resistive circuits) – look at diodes, voltage regulation, transistors – discuss impedances (cable, output, etc.) 05/10/25 basic electronics
- 3. The Basic Relations The Basic Relations • V V is voltage (volts: V); is voltage (volts: V); I I is current (amps: A); is current (amps: A); R R is is resistance (ohms: resistance (ohms: ); ); C C is capacitance (farads: F); is capacitance (farads: F); L L is inductance (henrys: H) is inductance (henrys: H) • Ohm’s Law: Ohm’s Law: V V = = IR IR; ; V V = = ; ; V V = = L L( (dI dI/ /dt dt) ) • Power: Power: P P = = IV IV = = V V2 2 / /R R = = I I2 2 R R • Resistors and inductors in series add Resistors and inductors in series add • Capacitors in parallel add Capacitors in parallel add • Resistors and inductors in parallel, and capacitors in Resistors and inductors in parallel, and capacitors in series add according to: series add according to: 1 C Idt 1 Xtot 1 X1 1 X2 1 X3 05/10/25 basic electronics 3
- 4. 05/10/25 basic electronics 4 Example: Voltage divider Example: Voltage divider • Voltage dividers are a classic way to Voltage dividers are a classic way to set a voltage set a voltage • Works on the principle that all charge Works on the principle that all charge flowing through the first resistor goes flowing through the first resistor goes through the second through the second – so V R-value – provided any load at output is negligible: otherwise some current goes there too • So So V Vout out = = V V( (R R2 2/( /(R R1 1 + + R R2 2)) )) • R R2 2 here is a variable resistor, or here is a variable resistor, or potentiometer potentiometer, or “pot” , or “pot” – typically three terminals: R12 is fixed, tap slides along to vary R13 and R23, though R13 + R23 = R12 always 1 2 3 R1 R2 V Vout
- 5. 05/10/25 basic electronics 5 Real Batteries: Output Impedance Real Batteries: Output Impedance • A power supply (battery) is characterized by a A power supply (battery) is characterized by a voltage voltage ( (V V) and an ) and an output impedance output impedance ( (R R) ) – sometimes called source impedance • Hooking up to load: Hooking up to load: R Rload load, we form a voltage , we form a voltage divider, so that the voltage applied by the battery divider, so that the voltage applied by the battery terminal is actually terminal is actually V Vout out = = V V( (R Rload load/( /(R R+ +R Rload load)) )) – thus the smaller R is, the “stiffer” the power supply – when Vout sags with higher load current, we call this “droop” • Example: If 10.0 V power supply droops by 1% Example: If 10.0 V power supply droops by 1% (0.1 V) when loaded to 1 Amp (10 (0.1 V) when loaded to 1 Amp (10 load): load): – internal resistance is 0.1 – called output impedance or source impedance – may vary with load, though (not a real resistor) V R D-cell example: 6A out of 1.5 V battery indicates 0.25 output impedance
- 6. 05/10/25 basic electronics 6 Power Supplies and Regulation Power Supplies and Regulation • A power supply typically starts with a transformer A power supply typically starts with a transformer – to knock down the 340 V peak-to-peak (120 V AC) to something reasonable/manageable • We will be using a We will be using a center-tap center-tap transformer transformer – (A’ B’) = (winding ratio)(A B) • when A > B, so is A’ > B’ – geometry of center tap (CT) guarantees it is midway between A’ and B’ (frequently tie this to ground so that A’ = B’) – note that secondary side floats: no ground reference built-in A B A’ CT B’ AC input AC output
- 7. 05/10/25 basic electronics 7 Diodes Diodes • Diodes are essentially one-way current gates Diodes are essentially one-way current gates • Symbolized by: Symbolized by: • Current vs. voltage graphs: Current vs. voltage graphs: V I V I V I V I 0.6 V plain resistor diode idealized diode WAY idealized diode no current flows current flows the direction the arrow points in the diode symbol is the direction that current will flow acts just like a wire (will support arbitrary current) provided that voltage is positive
- 8. 05/10/25 basic electronics 8 Diode Makeup Diode Makeup • Diodes are made of semiconductors (usually silicon) Diodes are made of semiconductors (usually silicon) • Essentially a stack of Essentially a stack of p p-doped -doped and and n n-doped -doped silicon to silicon to form a form a p-n junction p-n junction – doping means deliberate impurities that contribute extra electrons (n-doped) or “holes” for electrons (p-doped) • Transistors are Transistors are n-p-n n-p-n or or p-n-p p-n-p arrangements of arrangements of semiconductors semiconductors p-type n-type
- 9. 05/10/25 basic electronics 9 LEDs: Light-Emitting Diodes LEDs: Light-Emitting Diodes • Main difference is material is more exotic than silicon used in ordinary Main difference is material is more exotic than silicon used in ordinary diodes/transistors diodes/transistors – typically 2-volt drop instead of 0.6 V drop • When electron flows through LED, loses energy by emitting a When electron flows through LED, loses energy by emitting a photon photon of of light rather than vibrating lattice (heat) light rather than vibrating lattice (heat) • LED efficiency is 30% (compare to incandescent bulb at 10%) LED efficiency is 30% (compare to incandescent bulb at 10%) • Must supply current-limiting resistor in series: Must supply current-limiting resistor in series: – figure on 2 V drop across LED; aim for 1–10 mA of current
- 10. 05/10/25 basic electronics 10 Getting DC back out of AC Getting DC back out of AC • AC provides a means for us to AC provides a means for us to distribute distribute electrical electrical power, but most devices actually power, but most devices actually want want DC DC – 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 AC • this is why battery orientation matters in most electronics • Use diodes to “rectify” AC signal Use diodes to “rectify” AC signal • Simplest (half-wave) rectifier uses one diode: Simplest (half-wave) rectifier uses one diode: AC source load input voltage voltage seen by load diode only conducts when input voltage is positive
- 11. 05/10/25 basic electronics 11 Doing Better: Full-wave Diode Bridge Doing Better: Full-wave Diode Bridge • The diode in the rectifying circuit simply prevented The diode in the rectifying circuit simply prevented the negative swing of voltage from conducting the negative swing of voltage from conducting – but this wastes half the available cycle – also very irregular (bumpy): far from a “good” DC source • By using By using four four diodes, you can recover the negative diodes, you can recover the negative swing: swing: A C B D AC source load input voltage voltage seen by load B & C conduct A & D conduct
- 12. 05/10/25 basic electronics 12 Full-Wave Dual-Supply Full-Wave Dual-Supply • By grounding the center tap, we have two opposite By grounding the center tap, we have two opposite AC sources AC sources – the diode bridge now presents + and voltages relative to ground – each can be separately smoothed/regulated – cutting out diodes A and D makes a half-wave rectifier A C B D AC source + load load voltages seen by loads can buy pre-packaged diode bridges
- 13. 05/10/25 basic electronics 13 Smoothing out the Bumps Smoothing out the Bumps • Still a bumpy ride, but we can smooth this out with a Still a bumpy ride, but we can smooth this out with a capacitor capacitor – capacitors have capacity for storing charge – acts like a reservoir to supply current during low spots – voltage regulator smoothes out remaining ripple A C B D AC source load capacitor
- 14. 05/10/25 basic electronics 14 How smooth is smooth? How smooth is smooth? • An RC circuit has a time constant An RC circuit has a time constant = = RC RC – because dV/dt = I/C, and I = V/R dV/dt = V/RC – so V is V0exp(t/) • Any exponential function starts out with slope = Any exponential function starts out with slope = Amplitude/ Amplitude/ • So if you want < 10% ripple over 120 Hz (8.3 ms) So if you want < 10% ripple over 120 Hz (8.3 ms) timescale… timescale… – must have = RC > 83 ms – if R = 100 , C > 830 F R C V
- 15. 05/10/25 basic electronics 15 Regulating the Voltage Regulating the Voltage • The The unregulated unregulated, ripply voltage may not be at the , ripply voltage may not be at the value you want value you want – depends on transformer, etc. – suppose you want 15.0 V • You You could could use a use a voltage divider voltage divider to set the voltage to set the voltage • But it would But it would droop droop under load under load – output impedance R1 || R2 – need to have very small R1, R2 to make “stiff” – the divider will draw a lot of current – perhaps straining the source – power expended in divider >> power in load • Not a “real” solution Not a “real” solution • Important note: Important note: a “ a “big load big load” means a ” means a small resistor small resistor value value: : 1 1 demands demands more current more current than 1 M than 1 M 1 2 3 R1 R2 Vin Vout Rload
- 16. 05/10/25 basic electronics 16 The Zener Regulator The Zener Regulator • Zener diodes Zener diodes break down break down at some reverse at some reverse voltage voltage – can buy at specific breakdown voltages – as long as some current goes through zener, it’ll work – good for rough regulation • Conditions for working: Conditions for working: – let’s maintain some minimal current, Iz through zener (say a few mA) – then (Vin Vout)/R1 = Iz + Vout/Rload sets the requirement on R1 – because presumably all else is known – if load current increases too much, zener shuts off (node drops below breakdown) and you just have a voltage divider with the load R1 Z Vin Vout = Vz Rload zener voltage high slope is what makes the zener a decent voltage regulator
- 17. 05/10/25 basic electronics 17 Voltage Regulator IC Voltage Regulator IC • Can trim down ripply voltage to Can trim down ripply voltage to precise, rock-steady value precise, rock-steady value • Now things get complicated! Now things get complicated! – We are now in the realm of integrated circuits (ICs) • ICs are whole circuits in small ICs are whole circuits in small packages packages • ICs contain resistors, ICs contain resistors, capacitors, diodes, transistors, capacitors, diodes, transistors, etc. etc. note zeners
- 18. 05/10/25 basic electronics 18 Voltage Regulators Voltage Regulators • The most common voltage regulators are the The most common voltage regulators are the LM78XX LM78XX ( (+ + voltages) and voltages) and LM79XX LM79XX ( ( voltages) voltages) – XX represents the voltage • 7815 is +15; 7915 is 15; 7805 is +5, etc – typically needs input > 3 volts above output (reg.) voltage • A versatile regulator is the A versatile regulator is the LM317 LM317 ( (+ +) or ) or LM337 LM337 ( ( ) ) – 1.2–37 V output – Vout = 1.25(1+R2/R1) + IadjR2 – Up to 1.5 A – picture at right can go to 25 V – datasheetcatalog.com for details beware that housing is not always ground
- 19. 05/10/25 basic electronics 19 Transistors Transistors • Transistors are versatile, highly non-linear Transistors are versatile, highly non-linear devices devices • Two frequent modes of operation: Two frequent modes of operation: – amplifiers/buffers – switches • Two main flavors: Two main flavors: – npn (more common) or pnp, describing doping structure • Also many varieties: Also many varieties: – bipolar junction transistors (BJTs) such as npn, pnp – field effect transistors (FETs): n-channel and p- channel – metal-oxide-semiconductor FETs (MOSFETs) • We’ll just hit the essentials of the BJT here We’ll just hit the essentials of the BJT here – MOSFET in later lecture B C E B E C npn pnp
- 20. 05/10/25 basic electronics 20 BJT Amplifier Mode BJT Amplifier Mode • Central idea is that Central idea is that when in the right regime when in the right regime, the BJT , the BJT collector-emitter current collector-emitter current is proportional to the is proportional to the base base current current: : – namely, Ice = Ib, where (sometimes hfe) is typically ~100 – In this regime, the base-emitter voltage is ~0.6 V – below, Ib = (Vin 0.6)/Rb; Ice = Ib = (Vin 0.6)/Rb – so that Vout = Vcc IceRc = Vcc (Vin 0.6)(Rc/Rb) – ignoring DC biases, wiggles on Vin become (Rc/Rb) bigger (and inverted): thus amplified out Rc Rb in Vcc B C E
- 21. 05/10/25 basic electronics 21 Switching: Driving to Saturation Switching: Driving to Saturation • What would happen if the base current is What would happen if the base current is so big so big that that the collector current got the collector current got so big so big that the voltage drop that the voltage drop across across R Rc c wants to exceed wants to exceed V Vcc cc? ? – we call this saturated: Vc Ve cannot dip below ~0.2 V – even if Ib is increased, Ic won’t budge any more • The example below is a good The example below is a good logic inverter logic inverter – if Vcc = 5 V; Rc = 1 k; Ic(sat) 5 mA; need Ib > 0.05 mA – so Rb < 20 k would put us safely into saturation if Vin = 5V – now 5 V in ~0.2 V out; < 0.6 V in 5 V out out Rc Rb in Vcc
- 22. 05/10/25 basic electronics 22 Transistor Buffer Transistor Buffer • In the hookup above ( In the hookup above (emitter follower emitter follower), ), V Vout out = = V Vin in 0.6 0.6 – sounds useless, right? – there is no voltage “gain,” but there is current gain – Imagine we wiggle Vin by V: Vout wiggles by the same V – so the transistor current changes by Ie = V/R – but the base current changes 1/ times this (much less) – so the “wiggler” thinks the load is V/Ib = ·V/Ie = R – the load therefore is less formidable • The “buffer” is a way to drive a load without the driver The “buffer” is a way to drive a load without the driver feeling the pain (as much): it’s feeling the pain (as much): it’s impedance isolation impedance isolation out R in Vcc
- 23. 05/10/25 basic electronics 23 Improved Zener Regulator Improved Zener Regulator • By adding a transistor to the zener By adding a transistor to the zener regulator from before, we no longer regulator from before, we no longer have to worry as much about the current have to worry as much about the current being pulled away from the zener to the being pulled away from the zener to the load load – the base current is small – Rload effectively looks times bigger – real current supplied through transistor • Can often find zeners at 5.6 V, 9.6 V, Can often find zeners at 5.6 V, 9.6 V, 12.6 V, 15.6 V, etc. because drop from 12.6 V, 15.6 V, etc. because drop from base to emitter is about 0.6 V base to emitter is about 0.6 V – so transistor-buffered Vreg comes out to 5.0, 9.0, etc. • I Iz z varies less in this arrangement, so the varies less in this arrangement, so the regulated voltage is steadier regulated voltage is steadier Vreg Rload Vz Vin Rz Z Vin
- 24. 05/10/25 basic electronics 24 Switching Power Supplies Switching Power Supplies • Power supplies without transformers Power supplies without transformers – lightweight; low cost – can be electromagnetically noisy • Use a Use a DC-to-DC conversion DC-to-DC conversion process process that relies on flipping a switch on and that relies on flipping a switch on and off, storing energy in an inductor and off, storing energy in an inductor and capacitor capacitor – regulators were DC-to-DC converters too, but lossy: lose P = IV of power for voltage drop of V at current I – regulators only down-convert, but switchers can also up-convert – switchers are reasonably efficient at conversion
- 25. 05/10/25 basic electronics 25 Switcher topologies Switcher topologies from: http://www.maxim-ic.com/appnotes.cfm/appnote_number/4087 The FET switch is turned off or on in a pulse-width-modulation (PWM) scheme, the duty cycle of which determines the ratio of Vout to Vin
- 26. 05/10/25 basic electronics 26 Step-Down Calculations Step-Down Calculations • If the FET is on for duty cycle, If the FET is on for duty cycle, D D (fraction of time on), (fraction of time on), and the period is and the period is T T: : – the average output voltage is Vout = DVin – the average current through the capacitor is zero, the average current through the load (and inductor) is 1/D times the input current – under these idealizations, power in = power out
- 27. 05/10/25 basic electronics 27 Step-down waveforms Step-down waveforms • Shown here is an example of Shown here is an example of the step-down with the FET the step-down with the FET duty cycle around 75% duty cycle around 75% • The average inductor current The average inductor current (dashed) is the current (dashed) is the current delivered to the load delivered to the load – the balance goes to the capacitor • The ripple (parabolic sections) The ripple (parabolic sections) has peak-to-peak has peak-to-peak fractional fractional amplitude of amplitude of T T2 2 (1 (1 D D)/(8 )/(8LC LC) ) – so win by small T, large L & C – 10 kHz at 1 mH, 1000 F yields ~0.1% ripple – means 10 mV on 10 V FET Inductor Current Supply Current Capacitor Current Output Voltage (ripple exag.)
- 28. 05/10/25 basic electronics 28 Cable Impedances Cable Impedances • RG58 cable is characterized as RG58 cable is characterized as 50 50 cable cable – RG59 is 75 – some antenna cable is 300 • Isn’t the cable nearly Isn’t the cable nearly zero zero resistance? And shouldn’t resistance? And shouldn’t the length come into play, somehow? the length come into play, somehow? • There is a distinction between resistance and There is a distinction between resistance and impedance impedance – though same units • Impedances can be real, imaginary, or complex Impedances can be real, imaginary, or complex – resistors are real: Z = R – capacitors and inductors are imaginary: Z = i/C; Z = iL – mixtures are complex: Z = R i/C + iL
- 29. 05/10/25 basic electronics 29 Impedances, cont. Impedances, cont. • Note that: Note that: – capacitors become less “resistive” at high frequency – inductors become more “resistive” at high frequency – bigger capacitors are more transparent – bigger inductors are less transparent – i (√1) indicates 90 phase shift between voltage and current • after all, V = IZ, so Z = V/I • thus if V is sine wave, I is cosine for inductor/capacitor • and given that one is derivative, one is integral, this makes sense (slide # 3) – adding impedances automatically takes care of summation rules: add Z in series • capacitance adds as inverse, resistors, inductors straight-up
- 30. 05/10/25 basic electronics 30 Impedance Phasor Diagram Impedance Phasor Diagram • Impedances can be drawn Impedances can be drawn on a complex plane, with on a complex plane, with pure resistive, inductive, and pure resistive, inductive, and capacitive impedances capacitive impedances represented by the three represented by the three cardinal arrows cardinal arrows • An arbitrary combination of An arbitrary combination of components may have a components may have a complex impedance, which complex impedance, which can be broken into real and can be broken into real and imaginary parts imaginary parts • Note that a system’s Note that a system’s impedance is frequency- impedance is frequency- dependent dependent R L Z Zr Zi 1/C real axis imag. axis