1. Electronics for physicists
Lecture 2
Electronics Basics
November 2018
Electronics for physicists

2. Electronics for physicists
Current and Charge
I: current in Ampere [A] = [C/s]
Q: charge in Coulomb [C]
t: time in seconds [s]
Comments
1 C = ∙ 1018 electrons
1 femtocoulomb = 1 fC ≈ 6000 electrons
November 2018
Electronics for physicists

3. Charge deposition of a MIP in Silicon
„Minimum Ionizing Particle“ (MIP)
A MIP produces 80 electron-hole-
pairs/μm in Silicon
Thus the signal charge in 300 μm
deep silicon is 4 fC
November 2018
Electronics for physicists

4. Electronics for physicists
Voltage
U = ∫E ds
U : voltage [V]
E : electric field strength [V/m]
s : distance [m]
We do care for E in detectors, however less in electronic circuits.
„Voltage is what makes the current flow“ will frequently do!
November 2018
Electronics for physicists

5. Electronics for physicists
Ohm‘s Law
R : resistance in Ohm [Ω = V/A]
Meaning of Ohm‘s Law
„Voltage makes the current flow“
Flow of current through resistor causes voltage drop across resistor I
𝑆𝑙𝑜𝑝𝑒= 1 𝑅 U
November 2018
Electronics for physicists

6. Electronics for physicists
Power
P : power in [W = VA]
Comment
In detector instrumentation the energy bill rarely matters
Getting the heat out and the power in is more critical
November 2018
Electronics for physicists

7. Electronics for physicists
SCT power cables
Example:
4 Ω cable resistance for 100 m Iong cables (one-way!)
1 A of current per each of 4000 modules
P = 4 Ω x 1 A2 x 4000 = 16 kW ! This power is lost by heating cables
November 2018
Electronics for physicists

8. Electronics for physicists
How to reduce power ?
The SVX2 chip helped find the top quark at FNAL near Chicago
SVX’
1990
SVX2
1996
SVX4
2002
SVX3
1998
Decreasing transistor size makes chips smaller
Adding new functionality and channels makes them bigger
Smaller feature size means smaller chip voltages and saves power!
(Not true for technologies below 65 nm and with increasing subthreshold current)
November 2018
Electronics for physicists

9. Electronics for physicists
Specific resistance
R : resistance in [Ω]
: specific resistance in [Ωm]
Resistance increases with length l and decreases with area A
The same goes for other structures eg. FETs
November 2018
Electronics for physicists

10. Electronics for physicists
Material mass in R.L.
Much of the detector „mass“ is cables
Radiation length of copper is 14.4 mm, R.L. of aluminum is 88.9 mm
Ideally it is much better to use aluminum cables
November 2018
Electronics for physicists

11. Kirchhoff‘s Laws
Kirchhoff‘s Current Law (KCL) Kirchhoff‘s Voltage Law (KVL)
Charge conservation Conservation of energy
Loop
Consider „nodes“
Consider „loops“
Currents entering the node
equal currents leaving the node
The sum of all voltage drops around the loop is zero
November 2018
Electronics for physicists

12. Resistors in series and in parallel
Parallel resistors
Same current through all series resistors: IR1 = IR2
Same voltage across all parallel resistors: VR1 = VR2
November 2018
Electronics for physicists

13. Electronics for physicists
There are 2 types of power supplies: voltage sources and current sources
Voltage source
Ideally, the voltage is constant and does not depend on the load current.
• RL is load resistance
• Ri is „intenal“ resistance
Power supply: Car battery: Mono-cell:
Voltage sources are at its best at:
„no load“
small load currents
constant current I
Slope = -1/Ri U
RL >> Ri
November 2018
Electronics for physicists

14. Electronics for physicists
Current source
The ideal current source supplies a constant current independently of the voltage at the load. Current sources are at its best at short-circuits. I
Slope = -Ri U
RL << Ri
November 2018
Electronics for physicists

15. Example: ABCN Readout IC
Current sources are much more frequent than you might think. Count them in this ASIC for a future ATLAS silicon detector (designer J. Kaplon, CERN).
November 2018
Electronics for physicists

16. Electronics for physicists
Voltage divider
The voltage divider is one of the most frequent circuit elements.
Assumptions:
R₁ and R₂ are relatively large.
the load current is small. U1
Loop U2
KVL:
November 2018
Electronics for physicists

17. The capacitor Capacitor symbol Capacitor equations: Comment
Sketch of a plate capacitor
Comment
Energy to charge and then discharge a capacitor:
Power to charge and discharge with frequency f:
November 2018
Electronics for physicists

18. Capacitance of a silicon sensor- +
20 mm
80 µm d
εR = εSi
Electrical field
Calculate C for A = 80 μm x 20 mm, d = 300 μm, ε0 = 8.9 x F/m and εR = 11.8 (silicon)
Assuming full depletion and ignoring neigbouring strips, we get C ≈ 0.56 pF
In reality; neighborings strips dominate and C = 1-2 pF/cm strip length
November 2018
Electronics for physicists

19. Capacitors in series and in parallel
Parallel capacitors
Capacitors in series
thus
November 2018
Electronics for physicists

20. Series and parallel- summary
Component
Series
Parallel
Resistors
Capacitors R
Increase
Decrease
Decrease
Increase
November 2018
Electronics for physicists

21. Discharging a capacitor
within 1 τ : discharge to 37% of U0
within 5 τ : discharge to 0.7% of U0
t = 0 U0
0.37 x U0
t = 0  Uc = U0 (Initial condition)
t > 0  exponential drop of voltage
t=
(seconds)
Slope =- 1/RC
The current (Ic) in the discharge at that instant is therefore:
Ic = IR with Ic = dq/dt= C dU/dt and U = IRR
Therefore we have U = -CR dU/dt , rearranging and integrating gives:
November 2018
Electronics for physicists

22. Charging a capacitor through a resistor
Charging a larger capacitance C takes longer
Charging through a larger resistance R takes
longer too
t = 0
t = 0  capacitor resembles “short circuit”
t = ∞  capacitor resembles “open circuit”
Uin
0.63 x Uin
Slope =1/RC
November 2018
Electronics for physicists

23. Charging a capacitor through a current source
Charging C with a voltage sources vs.
charging C with a current source
November 2018
Electronics for physicists

24. Electronics for physicists
Low-pass
KCL:
IC = IR
KVL:
Uein – UC – UR = 0
Loop
𝐼𝐶=𝐼𝑅→𝐶 𝑑𝑈𝐶 𝑑𝑡 = 𝑈𝑒𝑖𝑛 − 𝑈 𝐶 𝑅 →
First approximation Uc small
Low-pass filter is known as an integrator circuit
November 2018
Electronics for physicists

25. Electronics for physicists
High-pass
KCL:
IC = IR
KVL:
Uein – UC – UR = 0
Loop
High-pass filter is known as a differentiator circuit
November 2018
Electronics for physicists

26. Electronics for physicists
Inductor
Inductor equations:
Air core solenoid vs air core toroid
The inductance L of a finite-length solenoid is given by
with length l and solenoid cross section A
November 2018
Electronics for physicists

27. Electronics for physicists
Summary table
Component
Voltage
Current
Resistors
𝑈=𝑅𝐼
𝐼=𝐺𝑈
Capacitors
𝑈= 1 𝐶 𝐼 𝑑𝑡
𝐼=𝐶 𝑑𝑈 𝑑𝑡
Coils
𝑈=𝐿 𝑑𝐼 𝑑𝑡
𝐼= 1 𝐿 𝑈 𝑑𝑡
G = 1/R
November 2018
Electronics for physicists

28. Coils in series and in parallel
Parallel coils
thus
Same current through all series resistors: IL1 = IL2
Same voltage across all parallel resistors: VL1 = VL2
November 2018
Electronics for physicists

29. Series and parallel – summary
Component
Series
Parallel
Resistors
Capacitors
Coils R
November 2018
Electronics for physicists

30. Electronics for physicists
Inductor
Magnet coil M1 for KATRIN
B = 3.6 Tesla
Stored Energy: 0.8 MJ
Current: 300 A
Inductivity L: 16.7 H
Length: 3.3 m
Wire bond of a few mm length
Inductivity L: a few nH
Substrate
Wire bond
November 2018
Electronics for physicists

31. Discharging an inductor
Discharge of an inductor through a resistor
t = 0  IL = I0 (Initial condition)
t > 0  exponential drop of current Io
(seconds) →
Coil: exponential drop of current
Capacitor: exponential drop of voltage
November 2018
Electronics for physicists

32. Magnetizing an inductor
Loop
0.63 x Uein/R
(a) Electrical circuit with voltage source, inductor and resistor.
KCL:
Slope =R/L
𝐼𝐿=𝐼𝑅=𝐼𝑅𝐿
𝑈𝑒𝑖𝑛 =𝐿 𝑑𝐼 𝑑𝑡 +𝑅𝐼
KVL:
𝑈𝑒𝑖𝑛−𝑈𝐿 −𝑈𝑅=0
𝑑𝐼𝑅𝐿 𝑑𝑡 + 𝑅 𝐿 𝐼𝑅𝐿= 𝑈𝑒𝑖𝑛 𝐿
(b) Inductor current after switching on Uin.
𝐼𝑅𝐿= 𝑈𝑒𝑖𝑛 𝑅 (1− 𝑒 − 𝑅𝑡 𝐿 ) ,
t = 0  inductor resembles “open circuit”
t = ∞ inductor resembles “short-circuit”
November 2018
Electronics for physicists

33. Circuit response to a sequence of rectangular pulses
RL Low-pass filter  integration circuit
November 2018
Electronics for physicists

34. Time behaviour - summary table
Component
Energy stored
t = 0
t  ∞
Resistors
No memory
time independent
Capacitors
Electric charge Q
-> Voltage
Q = 0  U = 0: short-circuit
Q ≠ 0  U ≠ 0: voltage source
Q is constant
𝑑𝑄 𝑑𝑡 =𝐼=0: open-circuit
Coils
Magnetic field B
-> Current
B = 0  I = 0: open-circuit
B ≠ 0  I ≠ 0: current source
M is constant
𝑑𝐼 𝑑𝑡 =𝑈=0: short-circuit
November 2018
Electronics for physicists

35. Electronics for physicists
RC and RL t
Uein 𝑅
IRL
IRL = Uein 𝑅
t = 0  capacitor resembles “short circuit”
t = ∞  capacitor resembles “open-circuit”
IRL = 0 t
Uein 𝑅
IRL
t = 0  inductor resembles “open circuit”
t = ∞ inductor resembles “short-circuit”
IRL = 0
IRL = Uein 𝑅
November 2018
Electronics for physicists

36. RL low-pass and high-pass filters
Low-pass filter
integrator circuit R UR L
Uaus = UL
High-pass filter
differentiator circuit
Homework
November 2018
Electronics for physicists

37. Helmholtz theorem (Thévenin's theorem)
Linear networks may be complicated and contain a large number of resistors, voltage sources and current sources.
(See sketch at black board…)
The good news is:
Any net can be described as one ideal voltage source UTh and one (internal) resistance RTh .
What is the voltage across and the current through a load resistor connected between any 2 nodes of the net ?+
(Only power consumption may not be predicted correctly.)
November 2018
Electronics for physicists

38. Electronics for physicists
Voltage divider
How to calculate UTh and RTh ?
Uth corresponds to the output voltage of voltage divider network without load (RL = ∞).
All voltage sources are replaced by short circuits and all current sources by open
circuits. The load resistor is removed.
RTh is the resistance between the output terminals of the circuit thus modified.
November 2018
Electronics for physicists

39. Electronics for physicists
Norton's theorem
Any linear circuit can be simplified to correspond
to a single current source and internal parallel
resistance.
How to calculate INo and RNo ?
The derivation is analogous to the Helmholtz-Thevenin equivalent circuit.
1. I No corresponds to the output current of the original circuit with a short
circuit as a load.
2. All voltage sources are replaced by short circuits and all current sources by open circuits.
RNo is the resistor between the output terminals of the thus modified
circuit.
(It turns out that RNo = RTh and INo = UTh /RNo )
Norton`s equivalent circuit
November 2018
Electronics for physicists

40. The superposition principle (I)
Circuit with 2 voltage sources and 3 resistors.
Resistors are neither parallel or in series.
The circuit above is a superpostion of the load currents of the circuits below with
IL = IL1 + IL2 and UL = UL1 + UL2 . UL
IL1
Output circuit for superposition principle
IL2 IL
November 2018
Electronics for physicists

41. The superposition principle (II)
The superposition principle: equivalent circuits
The voltage source U1 and U2 , respectively, are replaced by a short circuit
November 2018
Electronics for physicists

42. Systems of linear equations
What is the voltage U30 and current across the load RL ?
Output circuit for linear system
KCL: From ∑ Ii = 0 (all currents Ii flow into the node 3) follows
KVL: From ∑ Uij = 0 follows and
3 unknown voltages U30 , U31 , U32
3 independent equations => This is soluble
The solution is (see next slide)
November 2018
Electronics for physicists

43. Electronics for physicists
Algebra
With we get: and
November 2018
Electronics for physicists

44. Electronics for physicists
Some waveforms
harmonic oscillation
square wave
step function
detector signal after pulse shaping by an RC-CR filter
November 2018
Electronics for physicists

45. Electronics for physicists
Harmonic signals
Voltage
Current
Voltage and current are in phase!
Voltage
=>
Current
Phase shift of 90°: voltage follows current!
November 2018
Electronics for physicists

46. Electronics for physicists
„Harmonic signals
Voltage
Current
with
=>
Phase shift of 90°: current follows voltage!
November 2018
Electronics for physicists

47. Time to complex plane - summary
𝑑𝐹 𝑑𝑡 →𝑗𝜔 𝐹
𝐹 𝑑𝑡 → 1 𝑗𝜔 𝐹
𝜔=2𝜋𝑓
Time-domain differentiation
becomes multiplication by frequency 𝑗𝜔
Time-domain integration
becomes division by frequency 𝑗𝜔
Component
Time domain
Complex plane
Resistors
U=𝑅𝐼
𝑈 =𝑅 𝐼
Capacitors
𝑈 =𝑗𝜔𝐿 𝐼
Coils
𝐼 =𝑗𝜔𝐶 𝑈
November 2018
Electronics for physicists

48. Electronics for physicists
Generalized Ohm's law
Resistor: Capacitor: Inductor: Impedances Z1 and Z2 in series: Impedances Z1 and Z2 in parallel:
Z : complex impedance
November 2018
Electronics for physicists

49. Representation of Z in the complex plane
November 2018
Electronics for physicists

50. Frequency behaviour - summary
Component
𝜔 ≈ 0
𝜔  ∞
Resistors
𝑈 =𝑅 𝐼
Frequency independent
Capacitors
𝐼 =𝑗𝜔𝐶 𝑈
𝐼 = 0
open circuit
𝑈  0
short circuit
Coils
𝑈 =𝑗𝜔𝐿 𝐼
U = 0
𝐼  0
November 2018
Electronics for physicists

51. RC and RL filters - summary
Circuit
Low-pass filter
High-pass filter RC RL
November 2018
Electronics for physicists

52. Resistance and inductance in series
Homework
Use:
and
Calculate:
and
for
November 2018
Electronics for physicists

53. Electronics for physicists
Solution
and
November 2018
Electronics for physicists

54. „Real“ resistors Maximum ratings Precision Temperature stability
Types and sizes
HF properties
Costs
Wired resistors
SMD resistors with ruler
November 2018
Electronics for physicists

55. Electronics for physicists
„Real“ resistors
Equivalent circuit
November 2018
Electronics for physicists

56. „Real“ capacitors Multi-layer ceramic capacitor (MLCC) November 2018
Electronics for physicists

57. „Real“ capacitors Examples of wired capacitors November 2018
Electronics for physicists

58. Cylindrical capacitors
November 2018
Electronics for physicists

59. Electrolytic capacitors
November 2018
Electronics for physicists

60. Equivalent circuit of a capacitor
ESR: equivalent series resistance
ESL: equivalent series inductance
For small ω, the capacitive term 1 ω𝐶 dominates.
For large ω, the term ωL dominates.
The frequency response of a capacitor is often more important than the exact value of its capacitance.
November 2018
Electronics for physicists

61. Electronics for physicists
Low-pass filter
Integrator or low-pass filter
November 2018
Electronics for physicists

62. Effect of a low-pass filter
arbitrary vertical position
no phase information shown
Low-frequency signals pass without change
High-frequency are signals attenuated
Output signal is delayed w.r.t. input at high frequencies
November 2018
Electronics for physicists

63. Electronics for physicists
Low-pass filter
Amplitude of output signal is frequency dependent
Phase is frequency dependent
Frequency of output equals frequency of input
November 2018
Electronics for physicists

64. Electronics for physicists
Decibel
log stands for logarithm to base 10
Definitions:
for power
for voltage and current
So far so good, but what about:
dbm or dbmA ?
Note:
November 2018
Electronics for physicists

65. Electronics for physicists
Bode plot (low pass)
tan φ = -ωRC
Bode plot:
amplitude of transfer function Z
in db vs. log f
phase of Z vs. log f
November 2018
Electronics for physicists

66. Electronics for physicists
Low pass
at f-3db Z is reduced to -
the slope of Z is -20 db/decade
November 2018
Electronics for physicists

67. Compensated voltage divider
November 2018
Electronics for physicists

68. Electronics for physicists
Bode plot (high pass)
November 2018
Electronics for physicists

69. RLC Oscillator Note the current source which drives the circuit
November 2018
Electronics for physicists

70. Electronics for physicists
RLC Oscillator
small output voltages for very small and large ω
maximum output voltages at
November 2018
Electronics for physicists

71. Electronics for physicists
RLC Oscillator
Bandwidth:
At ω1 , ω2 , amplitude is of maximum
Q factor is related to loss of energy per oscillation:
November 2018
Electronics for physicists

72. Electronics for physicists
Inductors
November 2018
Electronics for physicists

73. Electronics for physicists
Inductors
Equivalent circuit
November 2018
Electronics for physicists

74. Capacitors and inductors in a nutshell
November 2018
Electronics for physicists