# Electronics. Basics & Applications. group talk Daniel Biesinger

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1 Electronics Basics & Applications group talk by Daniel Biesinger 1

2 2 Contents

3 Contents Basics Simple applications Equivalent circuit Impedance & Reactance More advanced applications - RC circuits Source-Drain Box Battery Box 2

4 Basics Current and voltage are crucial quantities Current law: Mesh rule: n I k =0 k=1 n V k =0 k=1 V and I are connected via Ohm s law: V = RI 3

5 Basics 1. Ohm s law Current and voltage are crucial quantities Current law: Mesh rule: n I k =0 k=1 n V k =0 k=1 V and I are connected via Ohm s law: V = RI 3

6 Basics Defined by Ohm s law: Symbol: In series: In parallel: R tot = 1 R tot = n Power dissipation: i R i n i 1 R i P = IV = I 2 R = V 2 4 R = V/I R [R] = kg m2 A 2 s 3 =Ω

7 Basics 2. Resistors Defined by Ohm s law: Symbol: In series: In parallel: R tot = 1 R tot = n Power dissipation: i R i n i 1 R i P = IV = I 2 R = V 2 4 R = V/I R [R] = kg m2 A 2 s 3 =Ω

8 Basics Defined by: Q = CV or I = C dv dt [C] = C V = A2 s 4 kg m 2 = F Symbol: In series: In parallel: 1 C tot = C tot = n n Cannot dissipate power i i 1 C i C i 5

9 Basics 3. Capacitors Defined by: Q = CV or I = C dv dt [C] = C V = A2 s 4 kg m 2 = F Symbol: In series: In parallel: 1 C tot = C tot = n n Cannot dissipate power i i 1 C i C i 5

10 Basics Defined by: V = L di dt [L] = kg m2 A 2 s 2 = H Symbol: In series: In parallel: L tot = 1 L tot = Stored energy: n i n i L i 1 L i E = 1 2 LI2 6

11 Basics 4. Inductors Defined by: V = L di dt [L] = kg m2 A 2 s 2 = H Symbol: In series: In parallel: L tot = 1 L tot = Stored energy: n i n i L i 1 L i E = 1 2 LI2 6

12 Basics Perfect voltage source: Maintains fixed voltage droop independent from load Symbol: Real voltage source: Can only supply a finite current = perfect voltage source with a small resistor in series 7

13 Basics 5. Current - and voltage sources Perfect voltage source: Maintains fixed voltage droop independent from load Symbol: Real voltage source: Can only supply a finite current = perfect voltage source with a small resistor in series 7

14 Basics Perfect current source: Maintains constant current regardless of load resistance Symbol: Real voltage source: Has maximum voltage it can supply = perfect current source with big resistor in parallel 8

15 Basics 5. Current - and voltage sources Perfect current source: Maintains constant current regardless of load resistance Symbol: Real voltage source: Has maximum voltage it can supply = perfect current source with big resistor in parallel 8

16 Basics How can one compare the relative amplitudes/strengths of two signals? Introduce the unit (deci)bel : db = 20 log A 1 A 2 Note: A 2 =2A 1 6dB In terms of power levels: db = 10 log P 1 P 2 Reference signal needed 9

17 Basics 6. The decibel scale How can one compare the relative amplitudes/strengths of two signals? Introduce the unit (deci)bel : db = 20 log A 1 A 2 Note: A 2 =2A 1 6dB In terms of power levels: db = 10 log P 1 P 2 Reference signal needed 9

18 Simple applications Output voltage is a certain fraction of the input voltage without load, current is the same everywhere I = V in R 1 + R 2 V out = R 2 R 1 + R 2 V in 10

19 Simple applications 1. Voltage dividers Output voltage is a certain fraction of the input voltage without load, current is the same everywhere I = V in R 1 + R 2 V out = R 2 R 1 + R 2 V in 10

20 Simple applications More sophisticated dividers use potentiometer V out = R 2 R 1 + R 2 V in 11

21 Simple applications 1. Voltage dividers More sophisticated dividers use potentiometer V out = R 2 R 1 + R 2 V in 11

22 Simple applications Real divider has a load attached R tot = R 2R L R 2 + R L + R 1 I = V in R tot V L = I R 2R L R 2 + R L V L = V in R 2 R L R 2 R L +R 1 R L +R 1 R 2 12

23 Simple applications 1. Voltage dividers Real divider has a load attached R tot = R 2R L R 2 + R L + R 1 I = V in R tot V L = I R 2R L R 2 + R L V L = V in R 2 R L R 2 R L +R 1 R L +R 1 R 2 12

24 Simple applications Some circuits perform calculations I = C d dt (V in V out )= V R V in (t) V out (t) dv out dt dv in dt V (t) =RC d dt V in(t) Output is prop. to rate of change/derivative of input 13

25 Simple applications 2. Differentiators Some circuits perform calculations I = C d dt (V in V out )= V R V in (t) V out (t) dv out dt dv in dt V (t) =RC d dt V in(t) Output is prop. to rate of change/derivative of input 13

26 Simple applications example: 14

27 Simple applications 2. Differentiators example: 14

28 Simple applications Exchange R and C in the differentiator circuit I = C dv dt = V in V out R V in (t) keep RC large V out V in V out (t) C dv dt V in R 15 V (t) = 1 RC t V in(t) dt + const.

29 Simple applications 3. Integrators Exchange R and C in the differentiator circuit I = C dv dt = V in V out R V in (t) keep RC large V out V in V out (t) C dv dt V in R 15 V (t) = 1 RC t V in(t) dt + const.

30 Equivalent circuit Every two terminal network of resistors and voltage sources can equivalently be represented by a single resistor Rth in series with a single voltage source Vth. 16

31 Equivalent circuit 1. Thévenin s theorem: Every two terminal network of resistors and voltage sources can equivalently be represented by a single resistor Rth in series with a single voltage source Vth. 16

32 Equivalent circuit How can one figure out Rth and Vth? Vth is the open circuit voltage Rth can be calculated by using the short circuit current: R th = V (open circuit) I(short circuit) 17

33 Equivalent circuit Open circuit voltage is given by Short circuit current: V in /R 1 V = V in R 2 R 1 + R 2 Rth is then given by: R th = R 1R 2 R 1 + R 2 18

34 Equivalent circuit Example: Voltage divider Open circuit voltage is given by Short circuit current: V in /R 1 V = V in R 2 R 1 + R 2 Rth is then given by: R th = R 1R 2 R 1 + R 2 18

35 Impedance & Reactance C, L are linear: output changes prop. to input Circuits with C and L have frequency dependence C, L change phase of input signal Impedance extends the concept of resistance to AC circuits, relative phase is taken into account 19

36 Impedance & Reactance 1. Problem C, L are linear: output changes prop. to input Circuits with C and L have frequency dependence C, L change phase of input signal Impedance extends the concept of resistance to AC circuits, relative phase is taken into account 19

37 Impedance & Reactance Take relative phase into account by using complex numbers Now and V,I C V (t) =Re(Ve iωt ) The Impedance is then defined as: Z = Z e iωt Z = R + ix ωt = φ 20

38 Impedance & Reactance 2. Solution Take relative phase into account by using complex numbers Now and V,I C V (t) =Re(Ve iωt ) The Impedance is then defined as: Z = Z e iωt Z = R + ix ωt = φ 20

39 Impedance & Reactance Impedance of R,C and L are given by: Z R = R Z C = 1 iωc Z L = iωl Ohm`s law is still valid: V = IZ Z tot = n i Z i (series) 1 Z tot = n i 1 Z i (parallel) 21

40 Impedance & Reactance 3. Impedance ZR, ZL, ZC and Ohm s law Impedance of R,C and L are given by: Z R = R Z C = 1 iωc Z L = iωl Ohm`s law is still valid: V = IZ Z tot = n i Z i (series) 1 Z tot = n i 1 Z i (parallel) 21

41 Output Impedance Impedance of the output of a circuit = int. resistance Limits the current that can by supplied to a load Very important for power supplies Cannot be measured with Ohmmeter Indirect measurement necessary 22

42 Output Impedance 1. Definition Impedance of the output of a circuit = int. resistance Limits the current that can by supplied to a load Very important for power supplies Cannot be measured with Ohmmeter Indirect measurement necessary 22

43 Output Impedance Output Impedance = Zi Measure Output voltage V without a load Use known load RL, measure the voltage VL over RL: V L = R L I and I = V Z i + R L Z I = R L V V L 1 23

44 Output Impedance 2. Measure Zi Output Impedance = Zi Measure Output voltage V without a load Use known load RL, measure the voltage VL over RL: V L = R L I and I = V Z i + R L Z I = R L V V L 1 23

45 Output Impedance Used to maximize the transferred power Design input impedance of load/output impedance of source Z L = Z S 24

46 Output Impedance 2. Impedance Matching Used to maximize the transferred power Design input impedance of load/output impedance of source Z L = Z S 24

47 RC-circuits Frequency dependent voltage dividers Ability to pass frequencies of interest while rejecting all other frequencies Usually one speaks of RC-filters Plenty of applications, therefore very important 25

48 RC-circuits Most common RC circuit, used e.g. in audio amp. 26 I = V in Z tot = = V in R + R V out = V in R + V in R + 1 iωc i ωc ω 2 C 2 i ωc R R ω 2 C 2

49 RC-circuits 1. High-pass filter Most common RC circuit, used e.g. in audio amp. 26 I = V in Z tot = = V in R + R V out = V in R + V in R + 1 iωc i ωc ω 2 C 2 i ωc R R ω 2 C 2

50 RC-circuits Amplitude of output signal: V out = V in R R /2 ω 2 C 2 27

51 RC-circuits 1. High-pass filter Amplitude of output signal: V out = V in R R /2 ω 2 C 2 27

52 RC-circuits Exchange R and C in the High-pass filter V out = V in 1 (1 + ω 2 R 2 C 2 ) 1/2 28

53 RC-circuits 2. Low-pass filter Exchange R and C in the High-pass filter V out = V in 1 (1 + ω 2 R 2 C 2 ) 1/2 28

54 RC-circuits Exchange R and C in the High-pass filter Can be used e.g. to eliminate interference 29

55 RC-circuits 2. Low-pass filter Exchange R and C in the High-pass filter Can be used e.g. to eliminate interference 29

56 RC-circuits Combinations of capacitors and inductors Very sharp frequency characteristic V in V out Z CL = i 1 ωl ωc ZCL and ZR act like a voltage divider 30

57 RC-circuits 3. Resonant circuit Combinations of capacitors and inductors Very sharp frequency characteristic V in V out Z CL = i 1 ωl ωc ZCL and ZR act like a voltage divider 30

58 RC-circuits Opposite behavior of C and L leads to: lim ω ω R Z CL Losses in C and L limit sharpness of the peak Used e.g. in radio amplifiers 31

59 RC-circuits 3. Resonant circuit Opposite behavior of C and L leads to: lim ω ω R Z CL Losses in C and L limit sharpness of the peak Used e.g. in radio amplifiers 31

60 Source-Drain Box Couple AC- and DC voltages Precise control over the amplitude of both AC and DC voltages Should not depend on frequency 32

61 Source-Drain Box 1. Intention Couple AC- and DC voltages Precise control over the amplitude of both AC and DC voltages Should not depend on frequency 32

62 Source-Drain Box AC DC 6.8kΩ 100 Ω 56Ω 50kΩ 4:1 Source Drain Ground 33

63 Source-Drain Box 2. Circuit AC DC 6.8kΩ 100 Ω 56Ω 50kΩ 4:1 Source Drain Ground 33

64 Source-Drain Box Voltage Divider 1: 1:122 Voltage DIvider 2: 1:501 Transformer: 4:1 Output is 1: of AC input DC input is divided by

65 Battery Box Simple to use voltage source (DC) Adjustable over wide range of voltages (1mV - 9V) + 1µF 10k 10k 9V + 90k 35

66 Battery Box 1. Intention Simple to use voltage source (DC) Adjustable over wide range of voltages (1mV - 9V) + 1µF 10k 10k 9V + 90k 35

67 Battery Box Standard 9V battery Potentiometer to adjust voltage Voltage divider to switch between ranges + 1µF 10k 10k 9V + 90k 36

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