# Electronics Electronic Components by tiz18123

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• pg 1
Electronics                                          Electronic Components
• most instruments work on either analog or digital             • Resistors: resists the flow of electron through a
signals                                                         circuit
• we will discuss circuit basics                                   – units of Ohms (Ω) with symbol =
– parallel and series circuits                                • Capacitors: resists changes in the voltage of a
– voltage dividers                                              circuit (capacitive reactance)
– filters – high-pass, low-pass, band-pass filters               – units of Faradays (usually μF or nF)
– with symbol =               OR
• the main purpose of this chapter is to get you to             • Inductors: resists changes in the current of a
understand the electronic filters                               circuit (inductive reactance)
– they help to reduce electronic noise                           – units of Henry’s (H) with symbol =
– less noise = a clearer signal (more on this in Chapt 5)

Resistors and Basic Circuit Laws                                                  Basic Circuits
• a few Laws to provide equations                              • series batteries
– (V = voltage, I = current, R = resistance)                   – voltage adds to produce a
– Ohm’s Law: V=IR                                                higher voltage
– Power Law: P = IV OR            P = V 2/R

• Kirchoff’s Laws
– current law: the algebraic sum of the current             • parallel batteries
around any point in a circuit is zero                        – currents add to add a higher
– voltage law: the algebraic sum of the voltages                 current capacity
around a closed electrical loop is zero

Basic Circuit                                             Voltage Dividers
• series resistors                                            • since the same
current goes
– resistance add directly                                     through each
RT= R1 + R2 + ...                                    resistor, there is
– same current through each                                   different
voltage drop
across each
• parallel resistors
– resistance add as reciprocals                             • the total voltage
1/RT= 1/R1 + 1/R2 + ...                                divides across
the series
– same voltage drop across each

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Example : a Voltage Divider                          Example : a Voltage Divider
• Calculate the magnitude of the voltages across     • Calculate the magnitude of the voltages across
each resistor                                        each resistor
• Steps to solve                                     • Steps to solve          V = 100. V
– calc. RT                                           – calc. RT             R1 = 50. Ω
R2 = 150. Ω
– calc. IT                                           – calc. IT             R3 = 250. Ω
– calc. each V        V = 100. V                     – calc. each V
R1 = 50. Ω                                            RT = 450. Ω
R2 = 150. Ω                 V = IT R T
RT= R1 + R2 + R3         R3 = 250. Ω
or IT = V/RT
RT= 50+150+250
RT=450 Ω                                             IT = 100. V/450. Ω
IT = 0.222 A

Example : a Voltage Divider                                  Current Dividers
• Calculate the magnitude of the voltages across      • since the voltage is the same across each
each resistor                                         resistor, the current across each is different
V = 100. V
R1 = 50. Ω                • the total current is divide across each parallel
V 1 = IT R 1                 R2 = 150. Ω                 path
V1 = (0.222 A)(50. Ω)        R3 = 250. Ω
V1 = 11.1 V = 11 V           RT = 450. Ω
•scan fig 2-3 on page 24
IT = 0.222 A
V 2 = IT R 2
V2 = (0.222 A)(150. Ω)
V2 = 33.3 V

V 3 = IT R 3
V3 = (0.222 A)(250. Ω)
V3 = 55.5 V

Example : a Current Divider                          Example : a Current Divider
• Calculate the magnitude of the current through     • Calculate the magnitude of the current through
each loop and the total current                      each loop and the total current

V = 100. V
R1 = 50. Ω
• Steps to solve                 V = 100. V
R1 = 50. Ω
I1=V/R1=100.V/50. Ω=2.0 A
R2 = 150. Ω           – calc. each I                 R2 = 150. Ω
– calc. IT                                    I2=V/R2=100.V/150. Ω=0.667 A
R3 = 250. Ω                                          R3 = 250. Ω
I3=V/R3=100.V/250. Ω=0.400 A

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Example : a Current Divider                                                 Loading Error
• Calculate the magnitude of the current through                    • making a measurement causes an uncertainty
each loop and the total current                                     in the measurement (analogous to the
Heisenburg Uncertainty Principle)

VM − Vx
Er =            × 100%
Vx

V = 100. V                                                                 − RS
R1 = 50. Ω
IT = I1+ I2 + I3= 2.0 + 0.667 + 0.400 A   Er =            × 100%
R2 = 150. Ω             IT = 3.066 A = 3.1 A                              RM + RS
R3 = 250. Ω

0

-10                                              •
% Error

-20
• Chopping (AAS)
-30

-40                                              • electrochemistry
-50
1,000            100,000        10,000,000     • electrochemistry
R M (Ω )

• The error drops as the internal resistance of the
meter increases

Inductors/Capacitors                                        RC Calculations
• Capacitors: resists changes in the voltage of a                   • reactance: the capacitor's equivalent to
circuit (capacitive reactance)                                      resistance
– units of Faradays (usually μF or nF)                             – there is a frequency dependence
– with symbol =               OR                                                       1    1
XC =        =
• Inductors: resists changes in the current of a                                         2πfC 2ωC
circuit (inductive reactance)                                     • impedance: the total “resistance” in an RC
– units of Henry’s (H) with symbol =                               circuit
– there is a frequency dependence
• AC signals are constantly changing, so                                                                    2
⎛ 1 ⎞
including these components in the circuit                                Z = R + X = R +⎜
2     2
C⎜ 2πfC ⎟
2
⎟
affects the signal                                                                      ⎝      ⎠

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RC Filters                                                                                          RC Filters
• At high freq. the capacitor becomes
• since this circuit is a voltage
practically a wire
divider                                                                                                    • its reactance goes down and no
– the voltage across the resistor is                                                                         voltage is dropped across it
R      R                R
VR = V ×      =V × =V ×
RT     Z                           2
⎛ 1 ⎞                                                                                            100%
⎜ 2πf C ⎟
R2 + ⎜

Voltage (% of input)
⎟                                                                                                                       VR
⎝       ⎠                                                                                        75%
VC
– the voltage across the capacitor is                                                                                               50%
⎛ 1 ⎞                    •   as f ↑, VR ?   ↑
⎜        ⎟
⎜ 2 πf C ⎟
25%
X            ⎝        ⎠               •   as f ↑, VC ?   ↓
VC = V × C = V ×                                                                                                                    0%
Z                         2          •   as f ↓, VR ?   ↓
⎛ 1 ⎞                                                                                                               10       100      1,000    10,000
2
⎜
R +⎜        ⎟
⎟              •   as f ↓, VC ?   ↑                                                                             Signal Frequency (Hz)
⎝ 2 πf C ⎠

RC Circuit Distortion                                                                                       RC Filters
• Distortion is dependent on the size of RC                            • See homework problems

RC Circuits                                                                                RC Circuits
• the capacitor cause a time lag in the voltage                         • the phase shift is frequency dependent,
(phase shift)       dV                 ⎛ 1               ⎞              decreasing as the frequency increases
i=C                           ⎜ 2 πf RC ⎟
φ = arc tan ⎜         ⎟
dt                    ⎝         ⎠
Phase Shift (degrees)

12
R = 1 kΩ
C = 1 nF
8
⎛ 1 ⎞
4                ⎜ 2 πf RC ⎟
φ = arc tan ⎜         ⎟
⎝         ⎠
0
100                     10,000                  1,000,000     100,000,000

Signal Frequency (Hz)

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Electronics Definitions                                Other Components
• resistance ≡ how a resistor effects a circuit     • diode ≡ allows current to flow in only one
direction; used in regulators
• reactance ≡ how a capacitor or inductor effects   • transitors ≡ can act as an amplifier or switch
a circuit                                           – replaced the vacuum tube
• transformer ≡ converts one AC voltage to others
• impedance ≡ the combination of resistance and
reactance                                         • rectifier & filter ≡ converts AC to DC
• regulator ≡ prevents surges in current from
changing the voltage of a power supply
• oscilloscope ≡ a device to read and analyze signal
and circuits

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