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Z - Circuit Theory > Impedance and phasors > Flashcards

Impedance and phasors Flashcards

1
Q

What is symbol and unit for impedance?

A

Symbol: Z
Unit: Ohms, Ω

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2
Q

When does impedance apply?

A

Only for time dependent circuits.

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3
Q

What is the equation to find Impedance of a component in a time dependent circuit?

A

V/I = Z

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4
Q

How do you combine time dependent circuitry and non time dependent circuity into a single impedance?

A

Impedance = Resistance + j×Reactance

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5
Q

What is the real part of impedance?

A

Resistance

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6
Q

What is the imaginary part of impedance?

A

Reactance

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7
Q

What is the equation for the reactance of a capacitor?

A

Xc = -1/ωC

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8
Q

What is the equation for the reactance of an inductor?

A

Xl = ωL

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9
Q

What is the equation to combine impedances in parallel?

A

Z = Z1Z2/(Z1 + Z2)

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10
Q

What is the equation to combine impedances in series?

A

Z = Z1 + Z2

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11
Q

What is the equation for an impedance potential divider?

A

The same as a normal potential divider.

Vout = Vin×Z2/(Z1+Z2)

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12
Q

What is H(ω)?

A

The transfer function

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13
Q

What is the transfer function?

A

This is the ratio of the output voltage to the input voltage.
Given by the equation:
H(ω) = Vout/Vin

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14
Q

What is the maximum power transfer theorem?

A

Maximum power is transfered when the source impedance is the complex conjugate of the load impedance.
Zs* = Zl

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15
Q

With regards to the maximum power transfer theorem, what can be said about the source and loads resistance and impedance?

A 
Rl = Rs
Xl = -Xs
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16
Q

What is active power?

A

This is the actual power dissipated by the circuit

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17
Q

What is reactive power?

A

Useless power that moves back and forth between source and load

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18
Q

What is the equation for the active power delivered to the load when the Load impedance is matched with the source impedance?

A

Pl = (Vrms^2)/4Rs

Pl = Active power from the load
Vrms = RMS voltage from the voltage source
Rs = Resistance fo the source
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19
Q

What are the axis and directions of them on an Argand diagram?

A

X-axis: Real part

Y-axis: Imaginary part

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20
Q

After the imaginary and real part of the voltage or current of circuit components in a circuit are drawn onto an Argand diagram, How do you calculate the voltage or current of the power source?

A

By combining the imaginary and real part vectorally

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21
Q

What are the 2 equations for the impedance of a capacitor?

A 
Z = jXc
Z = -j/ωC
22
Q

What are the 2 equations for the impedance of an inductor?

A 
Z = jXl
Z = jωL
23
Q

Where there is an imaginary and real vector for voltage or current involving resistances and impedances, how can the impedance be calculated vectorally?

A

Z = √(R^2 + X^2 )

24
Q

How would you calculate the angle of the magnitude of the voltage/current on an Argand diagram?

A

θ = tan^-1(Imaginary/Real)

25
Q

How is an RC filter set up?

A

You have a voltage input (source) connected to a resistor and capacitor in series

26
Q

What is the equation for the voltage across the resistor in an RC filter circuit?

A

Vr = Vin × ωτ / √( 1 + (ωτ)^2 )

27
Q

What is the equation for the voltage across the capacitor in an RC filter circuit?

A

Vc = Vin × 1 / √( 1 + (ωτ)^2 )

28
Q

How is an RC filter used as a lowpass filter?

A

The output voltage is across the capacitor.

29
Q

How is an RC filter used as a highpass filter?

A

The output voltage is across the resistor.

30
Q

For an RC lowpass filter, when the input frequency is a. High and b. Low what are the potential differences across the resistor and capacitor?

A

a. High: Potential difference across the resistor is high so capacitor (output) potential difference is low
b. Low: Potential difference across capacitor (output) is high and so the the potential difference across the resistor is low.

31
Q

For an RC highpass filter, when the input frequency is a. High and b. Low what are the potential differences across the resistor and capacitor?

A

a. High: Potential difference across the resistor (output) is high so the potential difference across the capacitor is low.
b. Low: Potential difference across the capacitor is high so the potential difference across the resistor (output) is low.

32
Q

How do you calculate the total input voltage from resistor and capacitor voltage? why?

A

Sum them together: Vin = Vr + Vc

Because Vc and Vr are complex voltages so we add them like vectors.

33
Q

How do you calculate the phase difference of current or voltage in an LRC circuit?

A

By calculating the angle from the real axis on the aground diagram to the magnitude vector of the voltage/current.
θ = tan^-1(imaginary/real)

34
Q

What is resonance and how does it occur?

A

This is a spike in amplitude that occurs when the periodic driving force oscillates a system at its natural frequency.

35
Q

How do capacitors store energy?

A

In an electric field

36
Q

How do inductors store energy?

A

In a magnetic field

37
Q

What happens in an LC circuit when you charge up a capacitor and then allow current to flow around the circuit?

A

Closing the circuit causes sinusoidal current between the inductor and capacitor which does not dissipate (ideally)

38
Q

What happens in an RLC circuit when you charge up the capacitor and allow the current to flow around the circuit?

A

Closing the circuit causes sinusoidal current between the inductor and capacitor which dissipates rapidly due to the resistor.

39
Q

When does resonance occur?

A

When the imaginary part of the impedance is equal to zero.

40
Q

Do the calculation to find the point of resonance for an RLC circuit

A 
Z = jωL + 1/jωC + R
Z = jωL - j/ωC + R
Z = R + j(ωL - 1/ωC)
ωL - 1/ωC = 0
ωL = 1/ωC
ω^2LC = 1
ω^2 = 1/LC
ω = 1/√LC
41
Q

How is a band-pass filter made?

A

By having an inductor-capacitor-resistor in series.

And measuring voltage across the resistor.

42
Q

What is the equation for an LCR band-pass filter?

A

Vout/Vin = R / (R+jωL + 1/jωC)

43
Q

What is the equation for the natural frequency of a band-pass/stop filter?

A

ω0 = 1/√LC

44
Q

What is the equation for the quality parameter?

A

Q = (1/R) × √(L/C)

45
Q

What is the equation for an LCR band-pass filter when using the equations for natural frequency and quality?

A

Vout/Vin = 1/√(1+(ω/ω0 - ω0/ω)^2 Q^2)

46
Q

What happens when ω0 = ω

A

Vout/Vin = 1
H(ω) = 1
This means that all the voltage is across the resistor

47
Q

How is a band-stop filter made?

A

Same as a band-pass filter: By having an inductor-capacitor-resistor in series.
And measuring voltage across the Capacitor-inductor.

48
Q

What is the equation for an LCR band-stop filter?

A

H(ω) = (√((ω/ω0 - ω0/ω)^2 Q^2))/√(1+(ω/ω0 - ω0/ω)^2 Q^2)

49
Q

What happens when ω0 = ω

A

Vout/Vin = 0
H(ω) = 0
This means that all the voltage is across the resistor and none is across the capacitor.

50
Q

What is a simple way to convert an inductor into natural frequency and quality factors?

A

√(LC) × √(L/C) = √L × √C × √L × √(1/C) = L × √(C/C) = L× √1 = L

√(LC) × √(L/C) = QR/ω0

L = QR/ω0

51
Q

What is a simple way to convert 1/capacitor into natural frequency and quality factors?

A

(1/√(LC))×√(L/C) = √(1/LC) × √(L/C) = √(L/LC^2) = √(1/C^2) = 1/C

(1/√(LC))×√(L/C) = RQω0

Z - Circuit Theory (3 decks)

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