electrical engineering

how do you calculate sensitivity

change in output/change in input

how do you calculate signal to noise ratio

$$SNR=20\log_{}\frac{signal_{-}level}{noise_{-}level}$$

how does a strain guage work

physical change changes the resistance of the gauge

what is the output voltage for a wheatstone bridge

how do diodes function

one side needs to be more positive than the other to allow current to go through

in a wheatstone bridge, how do you relate input voltage to vf

Vf=Vs/2

how do you find Vm in a wheatstone bridge

$$V_{m}=V_{S}\cdot\frac{R+\Delta R}{2R+\Delta R}$$

in a wheatstone bridge, how do you relate Vo to all the other voltages

$V_{o}=A\left(V_{m}-V_{f}\right)$ where A is amplifier gain

what is the output of an op-amplifier equal to

V_o=A(V₊-V_-) [difference between positive terminal input and negative input terminal]

what is the equation for gain in an amplifier

$$A=\frac{V_{o}}{V_{i}}$$

how do you find the voltage equations for amplifiers

remember what ideal means (voltages will be the same) then use KCL to derive voltage equations

what is impedance

$$Z=\frac{V}{i}$$

how do you find output impedance

ground inputs and apply test voltage at output then use facts of circuit (ideal or not)

how do inverting ideal amplifiers work

top one is ground but node voltage must be equal to Vi, use kcl

how do we know there is an output voltage?

amplifier is powered thus has its own power source!

what is meant by an ideal op-amp

no current in circuit, V_p=V_n

how do you solve an ideal op-amp circuit problem

vp=vn, source can have different voltages on each side, sum all voltages to find resistance and currents, use KCL to find Vo

what is the gain of a differential amplifier

$$A=\frac{R_2}{R_1}\left(V_2-V_1\right)$$

what is the common mode rejection ration equation

$$CMRR=20\log\left|\frac{A_{d}}{A_{c}}\right|$$

advantages of differential amplifier

high noise rejection, high CMRR

disadvantage of differential amplifier

low input impedance, difficult to adjust gain while maintaining resistor matching

advantage of instrumentation amplifier

amplify difference between two signals, high CMRR, high noise rejection, high input impedance, easy to change gain

disadvantage of instrumentation amplifier

more complex circuit thus more expensive

what is resolution

smallest change in input which is detectable

what is sensitivity

ratio of change in input to change in output

what is drift

gradual change in output due to external factor

advantage of wheatstone bridge

able to measure very small changes in resistance

what are the types of sensors

resistive, infrared, incremental optical encoder, ultrasonic, gyroscopes

what are signal conditioning circuits used for

amplify signals, rectify signals (ACDC), demodulate signals, filter signals

what are rectifiers

convert AC to DC signal. cannot use diode as they have significant voltage drop.

op-amp

difference between full-wave rectifier and half-wave rectifier

full-wave uses a half wave one and a summing one. half-wave only converts half of it, full wave converts all of it

what is a demodulator

used to extract original information (audio, video, digital data) from carrier wave at receiver. affected by signal amplitude and phase)

what is unique about demodulators

they use logarithmic op-amps rather than linear ones

what does low-pass filtering to in demodulators

get rid of high frequency components to find remaining dc components

what do filters do

allow to pass specific signal frequencies

low-pass filters

high-pass filters

2nd order butterworth low-pass filters

what is the reactance of a low pass filter capacitor

what is the relationship between voltages in a low-pass filter

what do low-pass and high-pass filters do respectively

low pass allows low frequencies to get through while high-pass allows frequencies above a certain amount

what magnitude is nano

$$1\times10^{-9}$$

what are the special cases for low pass filters

what are the special cases for high pass filters

what is the limitation for high-pass filters

there is a bandwidth limit which will limit the gain at high frequencies

what is the cutoff frequency for a butterworth low-pass filter

$$\omega_{o}=2\pi f_{o}=\frac{1}{\sqrt2RC}$$

what are the special cases for a butterworth low pass filter

what are signal conditioning circuits used for

amplify signals, rectify signals (AC to DC), demodulate signals (extract useful waveforms), filter signals (remove unwanted frequency)

what is the best sensor circuit practice

sensor output—>amplify—>filter

why do we amplify a signal before filtering

to maximise signal-to-noise ration (SNR) and minimise the noise of the system

noise added by filter and op-amps become less significant

what are pros and cons of butterworth compared to simple

better frequency removal but more expensive

what is a signal capture

converting analogue signal into digital signal

what output comes after wheatstone bridge + amplifiers

analogue signal

what does the signal capture process look like

MUX=multiplexers, SH=sample and hold, ADC=analogue to digital converter

what are multiplexers

set of switches use to select one from several analogue signals

what are the two types of multiplexer switches

FET CMOS, Reed relay

what is a FET CMOS switch

semiconductor switch that can be controlled with signal. electric field with current flow. cheap and simple but causes voltage drop, leakage, etc.

what is a reed relay

EM switch composed of two metals. when energised, em field from coil forces blades to close. low impedance and leakages but short lifespan

what is sample and hold? (S/H)

Analogue circuit made up of operational amplifiers used to hold a stable voltage V_o for time. when fet closed, c charged and then switch is opened

what is a digital signal

info stored in binary. Can be unipolar (positive values), bipolar (negative and positive with the negative sign being a 1 i.e. 11=-1), two complementaries (negative and positive values with sign represented by single bit), and binary-coded (each 4 bits represents a decimal number)

what is unipolar binary

16-bits can contain 2¹⁶ values, from 0 to 65,535

in two’s compliment, -32768 to 32768

what is an ADC

converts analogue to digital,

RC Charge, Flash, Successive Approximation, Ramp Compare, Dual Slope

what is operational procedure of Dual Slope ADC

1) clear counter

2) Close S1, open S2, C is charged by input voltage and counting starts

3) Intergrate for a fixed time

4) Open S1 close S2, start discharge C

5) de-integrate for a fixed time

6) stop when V_o=0

7) read count

what is the digital count equation for dual slope

x=N\frac{V_{\imaginaryI n}}{V_{ref}} where N = fixed number of counts during integration time (during charge)

what are the features of a Dual Slope ADC

accuracy determined by Vref and integration time, fixed ramp up time, fixed ramp down rate, slow, good for slow varying signals

what is a successive approximation

compare input signal to a signal generated by digital to analogue converter, tries bits from MSB to LSB. if too large, set back to 0, otherwise, keep 1

what is a dac

converts digital signal into analogue signal

current in each branch is fixed, positions of switches determine whether current runs through Rf

what is the relationship between V_o and D in DAC

$V_{o}=-V_{ref}\frac{D}{2^{N}}$ where D is digital value and N is number of bits

what is quantisation error

error in ADC/DAC as quantised in time and amplitude so signal measured wont be the same as original

max error in best case scenario is +-1/2 LSB

how to you calculate quantisation error

$$error=\frac{V_{range}}{2^{N}}\cdot0.5$$

how do you find the reactance of a circuit

$X=2\pi fl$ where f is frequency and l is inductance

what is the impedance equation

$$Z^2=R^2+X^2$$

how do you calculate current from impedance

$$I=\frac{V}{Z}$$

how do you calculate reactance from a capacitor

$$X=\frac{1}{2\pi fC}$$

how do we find direction of magnetic field

right hand curl rule

how to we find direction of force on wire

left-hand rule for motors, right-hand rule for generators

what does a brushed DC motor look like

what do the dots and x represent on the diagram

dot is current out of page towards you, x is current into page away from you (think of an arrow)

what are the magnet poles

south blue, north red

what is force equal to in a brushed DC motor

F = BIl where B magnetic field, I current, and L length of conductor

what is a torque constant of motor

Kt, involves Bld

what is torque for a machine

$$\tau=K_{T}I$$

how do you find back EMF of motor

$$W=\frac{Bld\omega}{2}$$

can also give constant for Bld

what is stall torque and no load speed respectively

stall torque when omega 0, no load speed when torque is 0

what happens when we decrease voltage in motor1

pushes graph down but still in linear fashion

what is main disadvantage of brushed motor

brushes need to be replaced as they wear down

where are we likely to find DC machines

small low cost things, electric vehicles, rc cars, fans

what are the 3 tests for dc motor

stalled motor 1, rotating motor, stalled motor 2

what does the first motor test do

clamp down to prevent rotation and plot v against I, gradient is R, y intercept is Vb

what does second motor test do

fixed voltage load motor up. plot emf against omega, gradient is KE

what does the third motor test do

range of voltage and increase load until stall, plot again

what is power equation including torque

$$P=\tau\cdot\omega$$

what does a brushless DC machine look like

what are brushless dc machines usually found in

electric vehicles, automation, consumer electronics

what is a wound field equivalent

using coils instead of metals to generate the magnetic fields

what are the comparisons between brushed and brushless dc machiens

what is the difference between DC machines and Permanent Magnet machines

PMSMs are driven using sinusoidal waveforms

comparison of PMSM and Brushless DC

difference between PMSM to induction motor

instead of pm or winding, usually have cage and short circuit so it is one block

what is the synchronous speed

$\omega_{s}=\frac{\omega}{p}$ where p is pole pair number