2P5 Electrical Engineering Flashcards
(131 cards)
1
Q
Where do electrons and holes go in a BJT?
A
electrons travel from emmitter to collector,
holes travel from base to emmittter
2
Q
What is hFE in a BJT?
A
IC/IB
3
Q
What are the performance limits for the BJT?
A
The linear limit (before saturation region)
Max Ic
Maximum power (I=1/V)
Maximum Vce
4
Q
What is hFE for a small signal model?
A
Current gain at constant VCE
𝜕𝐼C/𝜕𝐼B
5
Q
What is hoe
A
𝜕Ic/𝜕VCE
6
Q
What is hie?
A
dVBE/dIB
7
Q
What is hre?
A
dVBE/dVce (usually neglible)
8
Q
How does the small signal circuit change for pnp?
A
works the same, but things are reversed
9
Q
How can you make a common emmitter amplifier more stable?
A
Take R1 from the collector
10
Q
What is the advantage of adding emitter resistance?
A
Decreases the gain, but increases the stability of the DC operating point. But placing a capacitor in parallel can give large midband gain.
11
Q
Why is the instability of the operating point bad?
A
hFE can vary a lot (between 100 and 500), so VCE is very sensitive
12
Q
How does the emitter follower work?
A
It is a buffer, collector directly connected to Vcc, leads to unity gain
13
Q
What happens with a common mode signal in a differential amplifier?
A
Source voltages both rise the same amount, reducing gate source voltage, therefore small output
14
Q
How can common mode gain be model?
A
Split into two parallel circuits, with 2R3 in each one
15
Q
How can differential mode gain be modelled?
A
As no R3
16
Q
How does current mirror work?
A
Two BJTs, one with the collector connected to the base
17
Q
What is the gain with negative feedback with gain A and return ratio B?
A
gain = A/(1+AB)
18
Q
What is AB refferred to in negative feedback?
A
Loop gain.
19
Q
How does gain vary with a change in A for a negative feedback system?
A
dG/G = dA/A (1/(1+AB))
robust in variations in A
20
Q
How is bandwidth affected by feedback?
A
Lowers the 3dB frequency by (1+AB)
21
Q
What is the nature of gain bandwidth product?
A
Stays constant.
22
Q
How does negative feedback afffect input impedance and output impedance?
A
Rout decreases by a factor of 1+AB
Rin increases by a factor of 1+AB
23
Q
WHat’s the difference to an op amp whether it uses BJTs or FETS for the input differential pair?
A
FET has high Rin
BJT has high A and is stable, needs a constant current source.
24
Q
What are the rules for ideal op amps?
A
Output attempts to do whatever is necessary to make voltage difference between the inputs equal to zero
The inputs draw no current
25
What are input bias currents for op amps?
When input pair is a BJT differential amplifier, input bias currents are needed. For the 741, the currents are around 100nA. Leads to inaccuracy in outputs
26
What is the input offset voltage for a non-ideal op amp?
The voltage needed between inverting and non-inverting to drive output to zero.
27
What methods to solve non-ideal op amp?
Sum currents at the inverting input.
28
How does analogue adder work?
input resistances, then inverting amplifier.
29
How can you make an integrator with an op amp?
Using a capacitor in parallel with the op amp on an inverting amplifier set up
30
How can you make a differentiator with an op amp?
Capacitor before the op amp, and resistor in parallel with op amp.
31
What is a risk with the transimpedance amplifier?
Large R good for large amplification, however, parasitic C will reduce high freq response
32
What is a gyrator?
A component that acts like an inductor but can fit on a silicon chip.
Features 2 resistors and capacitor, inverting input connected to outpu
33
What is the maximum efficiency of a class A amplifier and how is this derived?
25%, it's derived from the AC power out/DC power in, which can be found from
Pout = vo^2/(2Rl)
Pin = VccIco
where Ico is the current flowing through the load.
34
What does the transfer characteristic of a class B amplifier look like?
Deadband (0V output) for -0.7V
35
How does a class B amplifier works?
When v1>0.7V, T1 is turned on and therefore conducts and begins to behave as an emitter follower. Reverse happens for v1<-0.7V with T2.
T1 is npn (normal)
but T2 is pnp
36
How does a class AB amplifier work?
placing diodes, which bias T1 and T2 base voltages to 0.7V and -0.7V respetively, this reduces the crossover distortion.
They need current sources (or mirrors) in order to hold the diodes at said voltages.
37
Conditions for oscillations?
AB = -1, therefore infinite gain and oscillations will occur
38
Define class A amplifier.
Transistors are always switched on
39
Conditions for balance in a three-phase load.
S,P,Q are all the same in every phase
40
Value of phase current and voltage for star and delta loads?
Star: Vl/root(3)
Il
Delta: Vl
Il/root(3)
41
Zdelta = kZstar
k=?
k=3
42
What is a synchronous machine made of?
Rotor -> brushes applying a DC voltage to produce a fixed field.
Stator -> 3 phases of coils wrapped around
43
What happens if you connect the stator coils in series?
Phase differences (due to positioning of coils) lead to less output, look at phasor diagram.
44
How do the windings work?
Balanced three phase currents flowing in a balanced three phase winding produce a rotating magnetic field.
45
What is the speed of rotation of a 2p-pole field?
ω/p, synchronous speed.
46
Conditions for steady conversion of energy?
Rotor and stator fields must have same number of poles.
Rotor and state fields must rotate at the same angular speed.
47
How does excitation voltage relate to thefield current?
E is proportional to the field current (rotor excitation)
48
What is Xs in a synchronous machine?
Synchronous reactance which is created by the stator drived field (proportional to stator current) which then creates back emf in the stator, due to self and mutual inductance.
49
How do you work out Torque of a synchronous machine?
prime mover power = electrical power out
=> T = 3VIcosφ/ω
where ω is the synchronous speed
50
What happens when the load angle reaches 90o in a synchronous machine?
Loss of synchronism occurs, safety margin is needed.
51
What do normally-excited, over-excited, under-excited phasor diagrams look like for synchronous machines?
Normally-excited -> Current in phase with voltage, perpendicular impedance phasor.
Over excited -> E is larger, so the current lags the voltage. Machine supplies VArs
Under excited -> E is smaller, machine absorbs VArs, under-excited
52
Do inductors absorb or create reactive power?
INductors absorb reactive power.
53
What is a synchronous compensator?
E is in phase with V, current is 90o out of phase.
If current lags voltage, then it is creating reactive power.
If current leads votlage, then it is absorbing VArs.
54
What are two types of rotor construction?
Cylindrical rotors for high sped machines
Salient pole rotor for low speed machines.
55
What limits the generator current?
Heating of stator coils due to resistance.
56
What limits generator voltage?
Limited by flux (iron losses, saturation) and insulation considerations.
57
How is real power controlled in transmission lines?
Controlled by the angle between the sending voltage and recieving voltage.
58
How is reactive power controlled in transmission lines and what are the consequences of this?
Controlled by the voltage difference between sending and recieving, this leads the line vunerable to voltage collapse or under voltage in the event that too much reactive power is drawn by the load.
59
What limits voltages on transmission lines?
Breakdown voltages can cause flashover.
transmission lines have largeee safety margins
60
What are two limits on power transfer over transmission lines?
load angle δ limited to 90o, and current is limited to minimise thermal losses I^2R.
The current limit depends on weather conditions.
61
What is the total rotational energy of the grid?
RKE = Kf^2
where K is the grid intertia constant.
PV,BESS,Wind does not contribute
62
What is the difference between demand and generated power?
Δ P = 2K f df/dt
63
What happens when reserve capacity is not enough to meet demand defecit?
LFDD - Low Frequency Demand Disconnection,
can disconnected up to 60% of peak london
64
How can reactive power be controlled on the grid scale?
voltage is +10% -6%
Excitation of synchronous geenrators is varied
Tap changing transforms used at bulk supply points, 33 different settings
Banks of capacitors can be switched on
Static VAR compensators.
Synchronous machines run as compensators.
65
What is the principle of operation of a 3-phase induction motor?
Stator wound with balanced three phase winding, creating a rotating magnetic field, which spins at synchronous speed ωs. Rotor spins at angular speed ωr. From the perspective of the rotor, the stator field is rotating at ωs- ωr. This leads to the creation of the rotor driven field at the same frequency as the induction motor.
66
How is an induction motor?
As a transformer, in stationary setting, but during rotation R2 -> R2/s, because E2 increases as E2 is proportional to ω
67
Define slip
s = (ωs-ωr)/ωs
where ωs is synchronous speed and ωr is rotor speed
68
What can you determine from a no-load test of an induction motor?
s->0, R2/s ->inf
therefore only consider magnetising reactance and the core loss resistance. Use the consumption of real power, can assume voltage is over R0 and Xm
69
What can you determine from a locked rotor test?
s=1, R2'/s is small, parallel components may be neglected, giving only series resistances and reactances. Again use consumption of real and reactive power based on phase current.
70
What two options are there for the core of an induction motor?
Wound rotor -> three phase windings similar to stator, has slip rings and brushes to enable addition of external resistances.
Cage rotor -> single conductor per slot, joined by thick conducting rings.
71
How does torque vary with slip?
01 electrical -> losses (plug braking)
72
How do you find max torque?
Ignore Xm and R0,, then use max power theorem, magnitude o fimpedances the same
73
What's the relationship between rotor resistance and torque?
Max torque stays the same, however, the slip at which max torque occurs increases with higher rotor resistance.
74
How do cage rotors maintain near constant torque?
Skin effect is exploited to change the rotor resistance. Low speed rotor, means high speed magnetic field in rotor leading to smaller cross sectional area, increasing resistance.
75
what is the relationship between β, ω, and c
c = ω/β = fλ
76
How can you model an ideal transmission line?
Inductor of length dx and capacitance per unit length dx connected to the ground.
77
What are the telegraphers equations?
dV/dx = -L dI/dt
dI/dx = -C dV/dt
which leads to wave eq with 1/c^2 = LC
78
How do coaxial cables work?
Voltage pushes oxillating current.
Charge pushed in creates an electric field whilst current produces a magnetic field.
E-field and H-field are perpendicular and produces an electromagneticwave perpendicular to both.
AS the wave propogates along the dielectric, it induces charge on the conductors
Induced charge sustains the E and H fields guiding it along the transmission line.
79
How do you model a lossy transmission line?
Compared to the ideal, add Rdx with Ldx, and in parallel with Cdx and conductance per unit length Gdx
80
Define Characteristic impedance Z0?
the ratio between voltage and current of a unidirectional wave at any point on a transmission line
81
How do you derive charactersitic impedance?
Z0 = VF/IF = β/ωC = sqrt(L/C)
82
What happens if the transmission line is lossy to the characteristic impedance?
It becomes frequency dependent.
83
How is the reflection coefficient ρL derived?
ZL = (VF+VB)/(IF+IB) at the load, then ZL = Z0 (VF+VB)/(VF-VB)
rearrange
ρL = VB/VF = (ZL-Z0)/(ZL+Z0)
84
What is VSWR?
Voltage standing wave ratio
Ratio of max voltage amplitude and min voltage amplitude
(|Vf| + |Vb|)/(|Vf|-|Vb|)
= (1+ρL)/(1-ρL)
85
What happens when a wave is reflected at an open circuit?
Infinite load resistance => reflection coefficient =1
=> antinode at the open circuit, perfect stnading wave
86
What happens if the wave is reflected at a short circuit?
0 load impedance => reflection coefficient is -1, get a π phase shift, creating a node at the reflection point.
87
What is the trasmission coefficient and how is it derived?
Voltages are not necessarily conserved at a junction, however currents are, use this property.
ρT = Z02/Z01 ( 1 - ρL)
ρT = 2Z02/(Z02+Z01)
88
What is the apparent impedance at any point of a line?
Z(x) = [Vf exp(~) + Vb exp(~)]/[If exp(~) + Ib exp(~)]
then Z(x=-l) = Z0 [ZL+jZ0tanβl]/[Z0+jZLtan(βl)]
89
What is quarter wave matching?
when l = λ/4, tan (βl) = inf
then Z(x) = Z0^2/ZL
then set Z0 = sqrt(ZLZin)
then no change in apparent impedance
90
What happens when a square pulse is passed down a transmission line?
Forward wave travels along to load, reflected with ρL,
this then travels back to the input impedance where is reflected back forwards with ρiρL
91
Derive the point form of the Gauss law.
integral over S (E.dA) = Q/ε
= integral over V ( ∇.Ε)dV = integral over V (𝜌.𝑑𝑉)/ε
=> ∇.Ε = ρ/ε
=> ∇.D = ρ
91
What is the Gauss law of magnetic fields and where does it come from?
∇.B=0
integral (B.dA) = 0, because flux lines have no beginning or ends, there are no monopoles for them to begin or end on.
92
What is the integral form of Farady's law?
integral ( E.dr) = - dΦ/dt
Φ= integral over S ( B.dA)
then
integral over c (E.dr) = integral over S (-dB/dt . dA)
where C is a closed curve, that bounds open surface S
Can use Stoke's theorem to get the differential form
93
How to derive differential form of ampere's law?
integral over C (H.dr) = integral over S (∇×H).dA = I = integral over S (J.dA)
=> ∇×H = J
94
Why is the differential form of Ampere's law wrong?
Doesn't account for displacement current, consider a capacitor, placing an amperian loop inbetween capacitor plates, shows no field.
Need to add a 𝜕D/𝜕t term, to account for this.
this ensures that the divergence is zero.
95
What conditions are applied for waves in a dielectric?
ρ=0 J=0
96
How is the wave equation derived for free space waves?
Take the curl of ∇×𝐄=−𝜕𝐁/𝜕t
and use the identity ∇×∇×u = ∇ ∇.u - ∇^2u
97
What is the refractive index in tersm of permittivity?
n = sqrt(εr)
98
Define plane wave.
Wave that propogates in a specific direction which if uniform in the plane perpendicular to the propogation direction
99
What is the impedance of a medium?
η = |E|/|H| = sqrt(μ/ε)
100
What is the vector N in electromagnetism?
N is the Poynting Vector
N = ExH, it is in the direction of propogation of the wave, magnitude is instantaneous power desntiy (time varying)
101
What is the average power per unit area of an electromagnetic wave?
|N| = |E||H|/2
or |N| = Erms Hrms
102
Define potential V
E = -∇V
V = - integral(Edx)
103
How is potential V related to charge density?
∇^2 V = -ρ/ε
Poisson equation
104
What is retarded electric potential?
V(r,t) = 1/4πε integral ( ρ(r0, t- |r-r0|/c)/|r-r0| dv)
105
What is the magnetic potential?
It is a vector such that
B = ∇xA
there are multiple options for A so it is set that, ∇.A =0
106
What is the magnetic equivalent of the Poisson equation?
∇^2A = -μJ
107
What is the magnetic equivalent of the retarded potential?
A(r,t) = μ/4π integral (J(r0, t-|r-r0|/c)/|r-r0| dv)
108
What is the half-dipole antenna?
a conductor of λ/4 sticking out of a ground plane, a.c. signal is applied which results in oscillating dipole and current, (method of images mean effective opposite charger being produced under ground plane)
109
How can you derive the expression for magnetic field strenght around a short dipole attena which has a cosine current?
Start with retarded potential.
r>>l => r-r0 = r
convert current density into current
Use complex notation and substitute ρ and z into the expression
Use the property that B = ∇xA
It should be entirely in the azimuthal direction
110
How can you derive the electric field strength around a short dipole antenna?
Switch B into spherical polar
Use the property that
∇×B = μεdE/dt
111
How do the field lines appear around a short dipole antenna?
MAgnetic field appears like lines of latitude
Electric field appears like lines of longitude
112
How do electrical fields and magnetic fields decay wrt distance from the antenna?
As 1/r, so that the Poynting vector can decay as 1/r^2
113
Define antenna gain
Gain = maximum power density/isotropic power density
114
Define radiation resistance?
The resistance that would need to be placed instead of the antenna that would dissapate as much power as the antenna radiates
Ra = P/I^2rms
115
How is radiation resistance affected by antenna length in relation to wavelength?
Ra is proportional to (l/λ)^2
116
What is true about an electrical field interfacing with a body with a different permittivity at an angle?
Dn1 = Dn2 (electric flux density normal to the body is conserved)
Et1 = Et2 (electric field tangential to the interface is conserved)
117
What is true about an electrical field interfacing with a body with a different permeability at an angle?
Bn1 = Bn2
Ht1 = Ht2
B and D both conserve normally
H and E both conserve tangentially
118
Define plane polarised wave?
With the plane, the electric field can take any direction within the plane, however, plane polarised means it is all in one direction
119
Give example of polarised wave usage
Radio & TV transmission
Sunglasses
Liquid crystal displays
120
Derive Snell law of refraction.
To ppreserve planes of peaks and troughs, must take same time for wave to travel distance λ1 in medium 1 and λ2 in medium 1
=> λ1/sinθ1 = λ2/sinθ2
then use refractive index
λ1=c/fn1
n1sinθ1=n2sinθ2
121
How do you derive the expression for how much of the electric field is reflected and how much is refracted?
Use the fact that the tangential component of E is conserved accross the boundary (Ei+Er = Et)
then use the fact that the tangential component of H is conserved,
Combine this with intrinsicc impedance to find Et/Ei
122
What is Brewster angle?
At brewster angle Er/Ei for the component of the electrical field parallel to the plane of incidence is not reflected. The reflected wave is plane polarised with the lectric field perpendicular to the plane of incidence
123
How do anti-reflection coatings work?
λ/4 layer of material which has geometric mean of impedances either side,
avoids trouble with apparent impedances, very similar to transmission line systems
124
How do you derive the wave equation for inside a conducting media?
ρ = 0
J = σE (Ohm's law)
add new term μσ 𝜕E/𝜕t
125
Define skin depth
δ = 1/α = sqrt(2/μωσ)
126
What approximation can be made in a highly conductive material?
σ>>ωε =>
α=β=sqrt(μωσ/2)
127
What is notable about the intrinsic impedanc eof a conductor?
It is complex so there is a phase difference between electric and magnetic fields
128
In a good conductor what is the pphase difference?
π/4
129
How do conducting surfaces respond to an incident wave from air at high frequency?
Nearly al is reflected as has very low intrinsic impedance.
130
