IA: 1P3: Analysis of Circuits and Devices Flashcards
What is the circuit symbol for an inductor?
What is the resistance of capacitors and inductors under DC conditions?
- Capacitors act like infinite resistance (open circuit)
- Inductors act like zero resistance (short circuit)
What is the Peak voltage, Vₚₑₐₖ?
The maximum amplitude of a voltage waveform
What is the peak to peak voltage, Vₚₚ?
The voltage difference between the maximum positive and maximum negative amplitudes of a waveform
What is the root mean square voltage, Vᵣₘₛ?
a measure of the effective value of an alternating voltage . It is the equivalent DC voltage that would produce the same amount of power in a resistive load as the AC voltage does over a complete cycle.
What is the equation for the root mean square voltage, Vᵣₘₛ?
For sinusoidal voltages and currents
Vᵣₘₛ = Vₚₑₐₖ / √(2)
For sinusoidal voltages and currents ONLY, other waveforms will have different factors
What is the general equation of a voltage waveform?
v(t) = V₀ + Vₘ sin(ωt +θ)
Vₘ = Peak voltage
What is DC offset, V₀?
A constant voltage component of a signal that shifts its entire waveform vertically from zero on the voltage axis
What is important to remember when analysing an AC waveform?
You should usually perform the DC and AC analysis separately (DC offset). This is important when considering things such as power generation adn distribution
What is impedance?
A measure of a components opposition to the flow of an alternating current (AC) in a circuit.
What is impedance represented by under DC conditions?
Resistance
What is the equation for electrical power?
P = IV = I²R = V²/R
What is ohm’s law for an AC circuit?
v = iZ
Z = Impedance
How can an AC potential divider be analysed?
The same as a DC potential divider, just using impedance rather than resistance
What is electrical admittance, Y?
a measure of how easily alternating current (AC) flows through a circuit, it describes the ease of current flow (rather than the opposition). It is the reciprocal of impedance
What is the equation for electrical admittance, Y?
Y = 1 / Z
What is electrical conductance, G?
A measure of how easily direct current (DC) flows through a circuit, it describes the ease of current flow (rather than the opposition). It is the reciprocal of resistance
What is the equation for electrical conductance, G?
G = 1 / R
What is the equation for the capacitance of a parallel plate capacitor with one medium between its plates only
What is the equation for the voltage across a charging capacitor in DC?
How can the equation for a sinusoidal AC voltage waveform be written in the compelx form.
Very important
no DC offset
What is the expansion of this:
What is the equation for the AC current through a capacitor?
What does this tell us about AC voltage and current through a capacitor?
There is a 90 degree phase difference between voltage (v) and current (i). The current is leading by 90 degrees
Plot a graph of AC voltage and current through a capacitor
How do you calculate AC power?
P = vi
Where v and i are the RMS values
What is the reactance of a capacitor, Xc?
Xc = 1 / ωC
What is the impedance of a capacitor in terms of reactance?
Z = -j Xc
What is the equation for the current through an inductor under DC conditions?
Derive the equation for the current through an inductor under DC conditions
What is the equation for AC current through an inductor?
What is the equation for AC voltage across an inductor?
What is the reactance of an inductor, XL?
XL = ωL
What is the equation for the impedance of an inductor in terms of reactance?
How can the imaginary component of impedance tell you if you are dealing with a capacitor or and inductor?
- If the imaginary component of Zₜ is positive, it is an inductor
- If the imaginary component of Zₜ is negative, it is a capacitor
As an inductor is not perfect, how can the imperfection be represented?
Through a series resistance which represents the resistance of the wire
As a capacitor is not perfect, how can the imperfection be represented?
Through a parallel resistance which represents the leakage current through the dielectric
Determine the amplitude and phase of the current, i, in this circuit:
amplitude = 2√(2)
Phase = -53.1 degrees
What is the circuit symbol for a DC voltage source?
What is the circuit symbol for an AC voltage source?
What does the arrow indicate on a DC voltage source?
It points to the highest potential / more positive side of the source
What does the arrow indicate on an AC voltage source?
It refers to the reference point for phase measurements relevant to that source
Explain the difference between an ideal and real voltage source:
An ideal voltage source has a constant voltage V₀ (or amplitude v) across its terminals and no resistance. A real voltage source would have a source resistance/impedance in series with the ideal voltage source
What is an ideal current source?
An ideal current source always produces the required current. An ideal current source will have an infinite internal resistance (or impedance).
Explain the difference between an ideal and a real current source
An ideal current source will have infinite internal resistance, a non-ideal source will have an internal resistance Rₛ in parallel with the source.
internal resistance is in parallel!
What is Thévenin’s theorem?
Any linear two-terminal network may be replaced by a voltage source Vₜₕ in series with a resistance Rₜₕ
linear means that this theorem does not apply to power
What is Norton’s theorem?
Any linear two-terminal network may be replaced by a current source Iₙ in parallel with a resistance Rₙ
linear means that this theorem does not apply to power
Identify the relationships between the different labels:
How would you find Vout for this circuit?
- You would convert the parallel circuits into their norton equivalents
- Combine the parallel current sources into a single combined current source
- Combine the parallel resistances into a single combined resistance
- Take the thevenin equivalent of the circuit and determine the resistance across the load
Determine the current I
I = 2mA
What is kirchoff’s voltage law?
The sum of the voltages around a closed loop must be zero
What are closed loops in a circuit known as?
Meshes
Create an expression with the voltages in this circuit:
V₀ = -V₁ - V₂ - V₃ - V₄
V₀ + V₁ + V₂ + V₃ + V₄ = 0
What is kirchoff’s current law?
The current flowing into any point of a circuit must be equal to the current which flows out of that point. In other words, the sum of current at every node must be zero
What are junctions in a circuit known as?
Nodes
How can you analyse a circuit using kirchoff’s laws?
- Mesh analysis
- Nodal analysis
They can be applied to both AC and DC circuits
How can you perform mesh analysis?
- Identify mesh currents which will cause every component to have at least one mesh current passing through it
- Consider each loop and form simultaneous equations using kirchoffs voltage law
- Solve to find the mesh currents
- You then have all the required values to solve the question
How can you perform nodal analysis?
- Label each of the nodes
- Assign one node as zero volts (if the circuit is grounded then there is already a defined earth point)
- Create an expression for each of the currents in terms of voltage using Ohm’s law
- Use Kirchoff’s current law to determine the unknown voltage
What is a bridge circuit?
Circuits used to measure unknown resistances, impedances, capacitances, or inductances by balancing 2 legs of a symmetric circuit. A bridge circuit consists of four branches that form a quadrilateral, with a source of voltage or current applied across one pair of opposite corners and a detection device connected across the other pair. At the balance point there will be no current through G and the 2 sides are at the same voltage
What is the impedance of a capacitor at DC (ω=0)?
infinite
What is the impedance of a capacitor at extremely high frequencies
tends to zero
What is gain?
What is the structure of a low pass filter?
A resistor and a capacitor in series with each other, with Vout across the capacitor
What is the equation for gain on a low pass filter?
Derive the expression for gain on a low pass filter
What does a plot of gain against frequency look like for a low pass filter?
What is the important transition point away from coarse analysis for the gain of a capacitor against frequency for a low pass filter?
Above the point where frequency starts to decrease the impedance of the capacitor. This point is defined as where the magnitude of the voltage gain is reduced by a factor of √(2), this is often known as the 0.7 or 70% voltage point. Similarly it can be defined in terms of power as the point at which the** ratio of input to output power is reduced by a factor of 2**, or in the decibel scale the log ratio is reduced by roughly 3 decibels.
What is the equation for the 0.7 voltage point on a low pass filter?
What is a bode plot?
a log₁₀ plot of the magnitude power/voltage gain against log₁₀ frequency
What is the equation for power gain in decibels?
What is the equation for voltage gain in decibels?
How can the decibel scale indicate gain or attenuation?
- Gain: Gain > 1 → positive Decibels
- Attenuation: Gain < 1 ← Negative Decibels
What is the equation for the magnitude of voltage gain?
What is the phase shift caused by a low pass filter given by?
What is the structure of a high pass filter?
What is the equation for gain of a high pass filter?
What is the equation for the magnitude of the gain of a high pass filter?
What is the equation for the 0.7 voltage point on a high pass filter?
The same as that on a low pass filter
What does a plot of gain against frequency look like for a high pass filter?
What is the gradient of the stop band of a gain against frequency for a low/high pass filter measured in?
dB/decade
Decibels are the units for the gain, a decade represents a tenfold increase or decrease in frequency.
What are the limitations of a first order filter?
The slope of the stop band is limited to 20dB/decade, many applications require a much higher cut off slope and therefore a higher order filter may be required
What is the relationship between the phase of AC voltage and current through an inductor?
There is a 90 degree phase difference between voltage (v) and current (i). The voltage is leading by 90 degrees
what is the phase difference between an inductor and a capacitor?
180 degrees
What is the structure of a series resonant circuit?
What is the equation for the voltage gain of a series resonant circuit?
What is the resonant frequency of a series resonant circuit given by?
What is the equation for the maximum voltage gain of a series resonant circuit when it is at resonance?
Derive the expression for the maximum voltage gain of a series resonant circuit at resonance:
What is the Q factor of a series resonant circuit?
The quality factor: it is ratio of the reactance to the resistance
What is the equation for the Q factor of a series resonant circuit?
- Q = 1/ω₀CR
- Q = ω₀L/R
- Q = |v₂|/|v₁| (only at resonance)
What can cause the quality factor of a resonant circuit to decrease?
- Imperfections in L or C increase the resistance and can reduce Q
What is the rule of thumb with Q values?
- Q > 10 is good
- Q < 1 is very bad
What is the bandwidth of resonance?
the range of frequencies over which the circuit can resonate effectively
What is the equation for the bandwidth of resonance?
What is the structure of a parallel LC resonant circuit?
How could you go about analysing a parallel LC resonant circuit?
Take the norton equivalent of the of the voltage source v1 and R1. You can then make all the components be in parallel by replacing R with an equivalent parallel impedance, RL.
What is the equation for RL in a parallel LC resonant circuit?
In terms of inductance, what is the equation for the Q factor in a parallel LC resonant circuit?
Where RL is the parallel equivalent impedance of the series impedance R
In terms of capacitance, what is the equation for the Q factor in a parallel LC resonant circuit?
Where Rᴄ is the parallel equivalent impedance of the series impedance R
What is a voltage amplifier?
A circuit designed to amplify the voltage of an input signal while preserving its waveform characteristics
What is the general model of a voltage amplifier?
“model” means that the more complicated circuit is simplified into just a few parameters
A = voltage gain
the whole circuit can be represented by just 3 parameters in this model
To which voltage amplifiers does this model apply to?
Amplifiers which have a linear gain, some amplifiers may have a gain which is a function of frequency and therefore cannot be represented by this model
For this amplifier model, what is the expression for the gain?
What is the rule of thumb for designing an amplifier circuit?
You often want a high input impedance (Rin) and low output impedance (Rout) as:
What is cascading amplifiers?
Cascading amplifiers is when you connect two or more amplifier stages in series to achieve greater overall gain whilst avoiding other problems (such as the miller effect)
What is a current amplifier?
A circuit designed to increase the current of an input signal
What is the model for a current amplifier?
Note: unlike a voltage amplifier, the output impedance is now connected in parallel with the current source
What is the expression for the current gain of a current amplifier?
What is the maximum power transfer theorem?
For a power amplifier driving a load RL with an output impedance Rout, the maximum power will occur when RL = Rout
How can you ensure the maximum power gain from an amplifier?
Match the load to the output impedance
For an amplifier, how is it possible that the output power can be greater than the input power?
where does the additional power come from?
The amplifier power supply, a DC source supploed the extra power delivered to the load as well as any power that might be dissipated in the internal circuit of the amplifier
What limits the voltage gain in an amplifier?
Since the additional power results from the amplifiers power supply, these power supplies (V+ and V-) set the maximum positive and negative voltage swing at output. If the gain is too high and the voltage tries to exceed the power supplies, it will be “clipped”, leading to distortion in the signal shape
What is the role of the capacitors which have been added to this voltage amplifier?
The capacitors will form basic RC filters, with C1 forming a high pass filter and C2 forming a low pass filter. This will restrict the bandwidth of the circuit and therefore the filter pair is often called a bandpass filter.
The capacitors could also have been placed at the output of the amplifier rather than the input
How do you handle a voltage amplifier with a bandpass filter?
It is assumed that the capacitors C1 and C2 have sufficiently different values and their effect on the frequency response is far apart enough so that they can be considered separately:
* Therefore when finding the low 0.7 frequency, you can completely ignore C2, treating it as an open circuit
* When finding the high 0.7 frequency, you can completely ignore C1, treating it as a short circuit
* When finding the midband gain you can perform the calculation using either scenario (usually much easier to use C1 as it is in series)
What is a semiconductor?
A semiconductor is a material that has an electrical conductivity between that of a conductor and an insulator. Its conductivity can be controlled by various factors, such as temperature and doping.
For example: Silicon is an insulator at low temperatures, but as temperature is increased it becomes more conducting. Its properties can also be dramatically altered by the incoroporation of dopant atoms in the crystal.
How does temperature effect the conductivity of a semiconductor?
Semiconductors, such as silicon, have stable covalently bonded structures. The electrons do not have enough energy to break free and move throughout the crystal at room temperature and so the semiconductor behaves like an insulator. As temperature increases, electrons can become free and so can move through the crystal, they also leave behind a hole on the silicon atom from where it came and this hole can also move throughout the crystal structure and so contributes to the current. Therefore, as temperature increases, resistance decreases, and conductivity increases
How do dopants effect the conductivity of a semiconductor?
Dopants are impurities added to the structure, this can add extra free electrons or holes to the structure. For silicon (which has 4 valence electrons) to add extra free electrons we dope with a pentavalent metal (P, As, Sb), and to add extra holes we dope with a trivalent metal (B, Ga, In). These extra free electrons/holes increase the conductivity of the semiconductor
What is an n-type semiconductor?
An n-type semiconductor is a type of extrinsic semiconductor which has been doped in order to increase the number of free electrons (negative charge carriers) and so increase the electrical conductivity. In the case of silicon, it is doped with a pentavalent metal.
What is a p-type semiconductor?
A p-type semiconductor is a type fo extrinsic semiconductor which has been doped in order to increase the number of holes (positive charge carriers) and so increase the electrical conductivity. In the case of silicon, it is doped with a trivalent metal.
What is the difference between an intrinsic and extrinsic semiconductor?
- An intrinsic semiconductor is pure semiconductor material with equal numbers of electrons and holes as charge carriers. Example: Pure silicon
- An extrinsic semiconductor is a doped semiconductor with impurities to increase conductivity. It has an imbalance of charge carriers (either more electrons in n-type or more holes in p-type)
What is a p-n junction?
A structure where the doping of a semiconductor abruptly changes from p-type to n-type. When the junction is formed, electrons and holes will diffuse from n to p-type and from p to n-type, respectively. This results in a region where there are no free electrons or holes, known as the depletion region. This produces an electric field which opposes difusion, the potential associated with this electric field is known at the contact potential.
What happens when you apply no external voltage to a p-n junction?
There is no net flow of current across the junction
What happens when you apply an external voltage to a p-n junction reverse biased?
Reverse biased is when you apply the external voltage such that the n-type will become more positive, causing more electrons to be removed from it and so increasing the size of the depletion region (hence holes are also removed from the p-type). The net current is known as the reverse saturation current, I₀.
How does a photodiode work?
A photodiode uses a reverse biased p-n junction as the reverse saturation current can be increased by exposure to light. Therefore photodiodes are engineered to allow light to access the junction.
What happens when you apply an external voltage to a p-n junction forward biased?
Forward biased is when you apply the external voltage such that the n-type will become more negative, causing fewer electrons to be removed from it and so decreasing the size of the depletion region (hence fewer holes are also removed from the p-type). The net current is then predominantly due to the diffusion current and is usually far larger than the reverse saturation current
How does a diode circuit symbol reflect the internal p-n junction?
The arrow indicates the direction of conventional current flow under forward biasing
What does a V-I graph look like for a diode?
How do LED’s work?
When a diode is forward biased, the electrons moving across the P-N junction can fall into empty holes from the P-type layer. This involves a drop from the conduction band to a lower orbital and so the electrons release energy in the form of photons. This happens in any diode, but only certain materials will produce photons of visible light.
How can you solve circuit problems with diodes?
You have to use graphical techniques to determine the operating point:
Plot the line for the current through the diode and plot this on the diode V-I graph, you can often use components in series with the diode and mesh analysis to determine the equation of this current. This plotted line is known as the load line
Note: the equation of this line is unique for each circuit!!
Determine the load line for this circuit
How can diodes be used in power systems?
As rectifiers
What are the 2 types of transistors?
- Field-effect transistor (FET)
- Bipolar junction transistor (BJT)
What is a Field-effect transistor (FET)?
A high-speed, low power transistor which is controlled by the input voltage as it uses an electric field to control the flow of current
What is a MOSFET?
A metal oxide semiconductor FET
What are the different types of MOSFET’s?
- n-channel enhancement
- n-channel depletion
- p-channel enhancement
- p-channel depletion
What is the gate voltage in an enhancement mode MOSFET?
positive
What is the gate voltage in a depletion mode MOSFET?
It can be positive or negative
What does the gate voltage in a MOSFET do?
it controls the flow of current from the drain to the source
What is the circuit symbol for an n-channel enhancement mode MOSFET?
- n-type: Arrow points towards the gate
- Enhancement mode: gaps in symbol
What is the structure of an n-channel enhancement mode MOSFET?
How does an n-channel enhancement mode MOSFET work?
If a voltage is applied between the drain (D) and source (S) when there is no gate voltage, then no drain current will flow as one of the p-n junctions will always be reverse biased and there are no charge carriers in the space between the drain and source.
If a positive gate voltage (VGS) is then applied, there will be an electric field between the gate and bottom of the device, attracting electrons towards the region between the gate oxide and p-type substrate (most of these electrons come from the n-type regions).
If VGS is high enough (above the threshold value, VT) enough electrons will accumulate to cause an inversion layer to form between the drain and source, forming an n-type conducting channel within the p-type. If you then a voltage between the drain and source (VDS) a current ID will flow from drain to source.
What are the 2 V-I graphs relevant to an n-channel enhancement mode MOSFET?
- ID (current between drain and source) against VDS (voltage between drain and source)
- ID (current between drain and source) against VGS (voltage between the gate and ground) in saturation
What does the ID (current between drain and source) against VDS (voltage between drain and source) graph look like for an n-channel enhancement mode MOSFET?
What does the ID (current between drain and source) against VGS (voltage between gate and ground) graph look like for an n-channel enhancement mode MOSFET when in saturation?
What is the circuit symbol for an n-channel depletion mode MOSFET?
- n-type: Arrow points towards the gate
- Depletion mode: NO gaps in symbol
What is the structure of an n-channel depletion mode MOSFET?
What is the difference in how an n-channel depletion mode and an n-channel enhancement mode MOSFET work?
A depletion mode MOSFET has a built-in n-type channel. The application of a positive gate voltage has the same effect as previously, however a negative gate voltage repels charge away from the cchanne, decreasing the conductivity.
What does the ID (current between drain and source) against VDS (voltage between drain and source) graph look like for an n-channel depletion mode MOSFET?
Note: VGS is now negative to turn off the FET
What is the structure of a common source amplifier?
What is a common source amplifier?
A type of amplifier configuration using a field-effect transistor (FET), where the source terminal is grounded and so is common to both the input and the output circuits.
What is the input impedance of a common source amplifier?
Ideally, it has infinite input impedance, however this is not very practical. Therefore normally the input impedance is usually very large (~MΩ)
For the below common source amplifier where the FET is an n-channel depletion type, what is the ID versus VDS graph?
Note: The operating point has been set such that VDS = VDD/2
What is VDS usually set at on a common source amplifier and why?
VDS = VDD/2
This is so there is the maximum voltage swing at the output. The value of RD then creates a load line and operating point
What do the different regions on this ID against VDS graph for a common source amplifier represent?
Different limiting factors which sets the safe operating region:
* A: non-linear, low resistance region
* B: Maximum limit of VGS
* C: Maximum power dissipation limit, (VDS * ID)max, hyperbolic curve
* D: Maximum values of VDS
* E: Safe operating region
Ideally the load line should cross diagonally through the safe operating region and the operating point should be as central as possible
What is the equation for gain on a common source amplifier?
What is a self-biased MOSFET amplifier?
A self-biased MOSFET amplifier is a type of amplifier circuit where the biasing of the MOSFET is achieved through feedback provided by a resistor connected to the source terminal.
How does a self-biased MOSFET amplifier work?
A self-biasing MOSFET amplifier uses a resistor (RS) in series with the source terminal to create a voltage drop, which sets the gate-source voltage (VGS). This establishes the operating point of the amplifier without requiring an external bias voltage source. The MOSFET is biased through feedback provided by RS, where the voltage drop across the resistor, caused by the source/drain current (ID), determines VGS.
What is the structure of a self-biased MOSFET amplifier?
Practical depletion mode MOSFET amplifier circuits use the self-biased amplifier where VGS is or needs to be negative
What is VGS given by for the following self-biased MOSFET amplifier?
How would you have to alter this design for a self biased amplifer if it were to be used by an enhancement mode MOSFET rather than a depletion mode MOSFET?
VGS must be positive if an enhancement mode MOSFET is being used. Therefore, the gate voltage is set by 2 resistors, R1 and R2 which form a potential divider, and then VGS is set by the difference between teh gate voltage and the source voltage (set by VS = RS * ID)
Note: The input impedance is now set by the parallel combination of R1 and R2
What is VGS given by in the following self-biasing amplifier?
