ELECTRONICS Flashcards
What is a mesh?
A loop that does not contain other loops
What is a KCL in regards to nodes
Sum of all current leading to a node = 0 (conservation of charge( so if all currents facing the node - the sum = 0 if some facing and some moving away then can rearrange to that sum of those moving away equal those going towards
Practice breaking circuits down into parallel and in series resistors
Know unit conversion (Charge, Voltage, Current and Powah)
Charge is in coulombs - 1.6E-19
Voltage is volts = 1 J/C
Current is I in amps - its C/s
Power is Watts and P = IV (also I^2 /R or V^2/I
(and of course V = IR
What is resistivity?
resisitivity is an inherent property of a material (unit is ohm m) - Resistance as a whole depends on geometry of as well as resistivity
So R = p *(L/A)
What is conductance?
Inverse of Resistance (1/R) - its G
Know how to calculate max wattage a resistor can take- eg 1000 Watt hair dryer - 120 V outlet - what can the max resistance be
W = IV so 1000 = 120 * I
I = 8.33
120 = 8.33 * R
R = 14.4
Difference between Ideal voltage and current source
Idea lvoltage source-
Output voltage doesnt change -
0 internal resistance -
Current changes based on load
Ideal current source -
Load doesn’t effect output current
(voltage changes based on load)
and infinite internal resistance
Branch vs node
branch a portion of circuit with 2 terminals
Node - a junction of 2 or more branches
What is KVL kirchoffs voltage law
Sum of the voltages around a closed loop is 0
eg so if have 2 sources their sum = 0
Know KCL and KVL in a circuit
So in series I is the same and V is the sum of V’s
R is the sum of the R’s
In parallel I is the sum, V is the same and R is(1/R = 1/R +1 /R + 1/R)(so int his case - conductivity is summed G is sum of G’s)
So what is voltage divider and how can it beused
Basicaly a bunch of things in series - if we have a bunch of resistors in series its a voltage divider - If there are a bunch of resistors in a row the voltage we measure can vary based on how much of the resistors we are measuring across
Whats a current ddivider -
A bunch of resistors in parallel
Practical vs ideal voltage source
Has internal resistance or impedance
But basically if the internal resistance is «< Rl (resistance of load) can essentially say that the vl = vs (voltage across load equals that of V source
Practical current source
internal imedance infinity - So the OUTPUT current depends on R - look at derivation for that - KEY HERE IN DIAGRAM THEN - our internal resistance is PARALLEL to our load resistance
So we see the opposite relationship where rs»> Rl then Is = Il(go through derivation)
How to measure voltage with a DMM (talk about loading error)
You want to do it in parallel with a resistor (in parallel voltage remains the same)
However to minimize loading error you want the DMM to have Very high resistance such that the R equivalent for this parallel part essentially just equals the resistance of the resistor in circuit
(DO OUT THE math - For our parallel section with the DMM the Req is 1/Req = 1/Rc + 1/Rdmm
Which turns into :Rc*Rdmm / (rc + RDmm)
SO if Rdmm»_space;> Rc then it just turns into Rc which is what we want - reflects the circuit
When measuring current with DMM what do we want
We want it in series with minimal resistance (so again thinking of resistance - in series add them up - soto make the equivalent resistance = the resistance in circuit want Rc»»> RDmm
Loading error equations fo measuring DC voltage
Essnetiall % error for V
(so V load - V battery / V battery)*100
OR for REsistor ITS different
-Rt / (Rt +Rm)
Note m is the load or meter and T is the soruce
NOTE always negative error because ITS always less than
NOTE -larger DMM resistance makes or error smaller
Measuring DC current error
% error for current again
and for Resistance
Er = - Rm/(Rn + RM) x 100
RM being fo the load I belive
LOADING ERROR DECREASES WITH SMALLER DMM RESISTANCE which we showed
Steps for KVL analysis
Draw current direction
Define clock wise or countercloskwise to sum voltages (use the same convention in every loop) - APPLY THE KVL (V in series should add up to 0 (or to the battery amount)
Or can apply kirchoff current law (at a node the sum of current s= 0
What is a Thevenin netwooork
Basically any network of sources and resistors can be seen as a voltage source and resistor in series (Vt is voltage source) and RT is resistance of netowrk
Norton Equivalent Circuit
Same idea as thevening but a CURRENT source and a parallel resistor - r = Rn
What is the relationship between Rt and Rn (thevenin and norton)
Rt = Rn
How to calculate Thevenin Resistance Rt
Take away voltage source replace with wire (note we’re calculating resistance Load sees) - so then we turn the remaining resistors into one equivalent resistor in regard to the load (in Voout or a b
Thevenin get the open circuit voltage
Remove the load Equal tot he voltage across the parallel resistor -
Calculate the Short circuit Current
See slide about how to do - go over study guide
How to generate Alternating Current
Current through a wire creates a magnetic field - you then have 2+ coils of wire placed so the changing magnetic field in one induces a voltage in the other - So basically we have an AC source we apply to one coil (energize it) - ti will create an AC voltage in the other coil
Why do we use AC over DC
motor and generator design simpler and more efficient
Whats the fourier theorm
Can construct any other waveform by adding sinusoid of different frequencies
What are the parameters of a sin wave
Frequency - 1/t # of cycles past a point in unit time0
w = 2 pi * f (rad/s) (angular frequency) (change in angle over time)
v = Vpsin wt (note Vp is peak V)
I = Ipsinwt (I is peak I?)
How does phase effect sine waves
Have 2 AC batteries - If both in phase - additive if one out of phase - subtract em
IV relationships in AC circuits how do they change (implications on power)
Not much really - V just becomes Vpsin(wt)
so if one resistor in a loop voltage across it is Vpsin(wt)
If want current across it its just (Vpsin(wt))/R
So for Power - P average = Irms * Vrms
Also can do Joule Heat in resistor (called effective DC signal)
CAPACITOR EQUATIONS
C = Q/V (q quantity of charge in coulombs) and C is capacitance in Farads
Q = CV
How does a capacitor work and what do they do
Important because means a VOLTAGE change can lead to a time varying charge (charge per time) (or current)
So we get a current change following our voltage change
How do capacitors add
inverse of resistors - so in parallel add them up - in series its 1/C = 1/C + 1/C
Does current flow through a capacitor?
NO in DC nothing - in AC its charging and discharign MIMIC the AC current
How does our capacitor react in regard to a sin wave
So if we’re thinking current - its share in Q charge over time - which equals CV (which is dV/dT because its not I its really dI/dT)
V we know varies with sin wave so we can make that
C dVpsin(wt) /dt
which if simplified becomes
wCVpcos(wt)
which is the equivalent to wCVpsin(wt + pi/2)
which is where we get the idea that OUR current is 90 degrees off from our voltage (current leads coltage0
How does current relate to Ip with sin wave
i = Ipsin(wt + pi/2) as such Ip = C*Vp
Given Ip = C*Vp what does that mean for reactance
that means C = Ip/Vp or 1/C = Vp/Ip which is we sub in Ip for wCVp - we get 1/wC
Which means our reactance is in fact frequency dependant
also w = 2 pi so
1/(2pifc)
How to get impedance of RC circuit (or derive it)
So this is a vector diagram where resistance is along the x and reactance is imaginary - down the y axis (negative ) - SO it’s just a right triangle
so Pythagorean - so its just ROOT( R^2 +C^2) which we have the specific equations for each
additionally if we want the angle for this vector its just arc tan (opposite over adjacent which is just C/R)
How do you make a low pass filter
have a capacitor in series with a resisto r(parallel to where measuring) - the idea being the signal at capictor cannot be low frequency or else circuit doesn’t work
Its a voltage divider so the voltage at the resistance is proportional (R/(R+C)
or R/Z
Can also do the same thing but measure across the capacitor
Whats BODE diagram
frequency repsonse vs magnitude (frequency against 20log(Vpo/VPin_
Complex # form
z = a +bi
a - is real part b is imaginary part (b is real # times root (-1)
in electronics use z = a +jb
z = a-jb is the conjugate
complex numbers in cmplex plane
a = abs(z)cos theta
b = abs (z) sin theta
abs z = root of a^2 + B^2)
so a is our x axis and b is our y axis
z is the sum
angle theta again is
arctan (B/A)
What is the polar conversion of z* = a- jb and z = a + jb
abs(Z)e^(jtheta) or abs(Z)e^(-jtheta)
When use cartesian vs polar
add subtract for cartesian - multilpy divide for polar
Voltage in ac circuuit
V = I*Z (see deri - dont need to know)
Voltage across capacitor vs voltage across resistor in RC circuit in terms of vs
vc is vs * (1/(jwrC+1)) vr is vs *((jwrc)/(jwrc+1))
How does frequency effect ouput?
changes current and voltage DUE to change in impedances - this is key for ATTENTUATION - is the term for this (jw/jw) - for passive circuit lesss than 1 - for active circuit - any value posibble
How do you define Vo and Vi when determining gain for a capacitor then a resisto rin series
Vi is Z and Vo is R (so its R/z which is jwrc / (1 + jwrc)
Gain function equation! for high pass filter?
wrc / (root(1 + (wrc)^2)
AND THETA = (PI)/2 - inversetan(wrc) (phase degree)
tALK ABOUT HALF POWER POINT - WHAT THINGS ARE TRUE DURING IT
so w = 1/RC (makes our wrc / (root(1 + (wrc)^2) equation 1/root(2)
That means gain is 1/(ROOT(2) or 0.707
essentially po/pi = 1/2
it’s -3db
phase angle is 45 degrees
what are the two types of BODE plots
magnitude plot - frequency in response to db or gain
and the PHASE plot - phase shift in regard to frequency
Low pass filter for gain vs high pass
low pass is R then C - high pass is C then R - so they essentially switch
Vo is Zx while V in is Z(C +R?) - which makes essentially the same equation but (1 / (ROOT(1+(wrc)^2))
BUT its the same in that when w = 1/RC we get our half power point
2nd order vs 1st oder filter comparisons
1st order 3db is half power point - loses 20 db per decade (hence log 20)
2nd order is double 6 is our half power point and lose 40 per decade
Describe basics of inductors
inductance is L
v = L *di/dt
measured in henrys
Enegry stored is
W = 1/2 (LI^2)
An inductor is a passive electronic component which is capable of storing electrical energy in the form of magnetic energy. Basically, it uses a conductor that is wound into a coil, and when electricity flows into the coil from the left to the right, this will generate a magnetic field in the clockwise direction.
How do inductors work in basic circuit addition
in series add, in parallel combine like resistances
What does inductor do in DC circuit
Is a wire
indcutvei resistance
jwl (zo overall Z(impedance) is R + jwl
General rule for determining what kidn of filter something is
I guess in parallel - the first determines filter type the second is used to build resistance (so a capacitor on the front means high end pass ) but if its second we want the signal that builds resistance so resitor then capacitor is low end pass
What is an RLC bandpass filter
lets through a certain band - C lets in high pass F only lets in low pass so get something in the middle (so L then C then R parallel to load
What is the max gain on an RLC band pass
when w = 1/(ROOT(LC))
Q factor of RLC
quality factor - indicates the selectivity of the circuit (basically like resolution - how narrow this peak is - its (w*L)/R
and typically adjust through R
How do you make a band stop filter?
essenitally like a band pass filter BUT you read across the L and C as opposed to the R (same idea ) - R means filtering nothing) - and we generate resistance across the two extremes
What is a semicondcutor
crystalline -conductivity between a conductor or insulator - all of outer electorns are PERFECT covalent bonds but we dope them to create holes and free electorns
N doped - means there is group V element - so free electrons
P doped - means group 3 elements and there is a hole!
What is the typical semiconductor interaction
we got a p junction and an N junction and essentially there is attraction at the junction - combining of electrons and holes - depletes oles in p region and electorns in n region near junction (builds up an electric field)
What is a forward biased vs reversed biased diode
forward bias can allwo current through - essentially the current goes into the p region (or + charge does) which pushes the holes of the p region to the junction which attracts the negative charge there allowing the positive charge to continue
IN a reverse biased - the negative charge goes to the p region and the holes are atttarcted to that (and vice versa) and you get DEPLETION - no interaction
Whats BJT -
bipolar hunction transistor - basically have a channel - so basically either PNP or NON - emitter base and collector - can tell direction because it always goes P to N
What is current gain
Beta = Ic/Ib
Collector current is controlled by BASE current - so as w change base current the collector current is modified
Genereal relationships between base cu[rrent and coelctor current
a smaller base current effects the collector current more so greater gain
Key Points about MOSFETS
- FETs are widely used in both analogue and digital circuits
- They have high input resistance
- There are two basic forms of FET: MOSFETs and JFETs
- MOSFETs may be divided into DE and Enhancement types
- In each case the gate voltage controls the current from the drain
to the source - The characteristics of the various forms of FET are similar except
that they require different bias voltages - FETs can be used to produce various forms of amplifier and a range
of other circuit applications
OPAMP - ideal input impedance is?
infinity! - because we can see the thevenin form - where its read across R in - BUT the amount of voltage that goes to r in is split across r in and r input (Rs) so if Rinput is massive- these spit essentially becomes all for r input and not for input resistance
What is the amplifier output resistance
Shoudl be 0 for kidn of the opposite reason - what the amplified v out to be 100% of V in and again its split and want it to all be across our Rl
What are the characteristic sof op amp
hugh voltage gain, high inut impedance and low output impedance
Whats the problem with just traditional op amps -
no flexibiltiy and cvery low voltage range - maxes out very ease v+ to v- is small (also not stable and linear (NEED FEEDBACK
What are some basic neg feedback loop equations
Ao open look voltage gain = vo/v’ (v’ being adjusted input)
v’ = vi = Bvo (B being the fraction of vo fed back
Af = Ao/(1+AoB)
with Af being the actual gain and Ao being initial gain
Af = 1/B (typically assuming that AoB»»1
Why are negative ffedback opamps good
CIRCUIT PROPERTIES ONLY DEPEND ON EXXTERNAL FEEDBACK NETWROK SO SUPER CONTROLLABLE(
also helps with non linearity improves response etc)
Types of OPAMPS
if the negfeedback loop is wire - THIS IS A BUFFER - just used to minimize loading error due to high input impedance and low output impedance (voltage follower)
Current follower = Have input as current source and a resistor on feedback loop
VIRUTAL common potential (V+ = V-) Essentially NONE of the current goes to opamp but goes to resistor (iF»_space;iB) so ii = if
vo = -if*Rf 9dependant on feedback loop)
Ri = Rf/A (input resistance )
INVERTIN AMP -has a resistor before the invert input
Close loop gain - Af = -Rf/Rs = (vo/vs)
here is = -if which is essentially the same as before
so
vo = -RF/RS * vs
Voltage ADDER -its a combo adder and multiplier - the adders are in parallel and each factor is multiplied by what we stated before rf/rs
Explain current follower
Current follower = Have input as current source and a resistor on feedback loop
VIRUTAL common potential (V+ = V-) Essentially NONE of the current goes to opamp but goes to resistor (iF»_space;iB) so ii = if
vo = -if*Rf 9dependant on feedback loop)
Ri = Rf/A (input resistance )
Explain inverting amplifer omp amp
INVERTIN AMP -has a resistor before the invert input
Close loop gain - Af = -Rf/Rs = (vo/vs)
here is = -if which is essentially the same as before
so
vo = -RF/RS * vs
Explain adder
Voltage ADDER -its a combo adder and multiplier - the adders are in parallel and each factor is multiplied by what we stated before rf/rs
OP AMP INTEGRATOR
also has a capacitor in parallel with the feedback loop reset switchch (also has a hold switch)
dvo/dt = vC*R
Vo = 1/RC * integrated (vidt)
takes a square wave and makes it min max wave (I forget the name)- basically since integrates give the slope - so good as waveform generator
OP AMP DIFFERENTIATIOR
Here the capacitor is before the op amp
Vo = -RC Dvi/dt
Basically only spikes when there is a change in signal
NON INVEFRTING AMPLIFIER -
goes in both + and negative both have a reistor before
NOTE source at Positie
Gain = 1 + Rf/Rs
again dependant on the top one
WHY INERTI OR NON INVERTINY
NON INVERTING HAVE HIGH INPUT IMPEDANCE inverting typically low input impedance
Differential siubtractor amp
OK so 2 inputs each has a resistor - Positive goes to ground and negative goes to vo out
if BOTH change together its common mode - if change independently - normal mode
a GOOD ONE HAS A HIGH CMMR - common mode reject ratio
v out - Rf/Rs (vs - v1)
CMMR = Ad/Acm
So better CMMRR means better at rejecting common mode signal - useful for removing noise
Ad is ratio of vo compared to (v2-1)
and Acm is ratio of Vo to V2
INSTRUMENT AMPLIFIER
start with 2 op amps go into one
Golden rules of neg feedback
voltage at input is the same and no current to op amp (except when sat)
How does frequency effect opamp gaine
Af *fo = ft - as it goes up - gain goes down until it reaches unit - NO GAIN
What is SLEW
s = dv/dt - basically the idea that there’s lag - vo out doesn’t match vi immediately
can deal with slew issues by decreasing frequency, lowering A (gain) or lowering in put signal
Positive vs negative feedback loop
changes where it goes - if loop on positive its positive if its on invertor its negative which makes sense
positive feedback use
to staurate - get max (eg turns sin wave into max) or also to dea with noise -very much like a binary on off switch
