08 - oscillating circuits

What’s a four-terminal network?

• network with 4 connections

• Similar to a voltage divider

• Input & output are complex

• The focus is on the relationship between the input and the output

What’s the relationship between the input & the output in a four-terminal network? (Formula)

How is this ratio called?

What are the 2 parts of this formula?

• A complex = Uout complex sur Uin complex = formule avec exp

• Transfer function

• Uout/Uin = amplitude response

• Delta phi = phase response

What’s an RL series circuit?

A circuit with a resistor and an inductor in series

Which circuits configurations are a high pass? A low pass?

High pass :

• RL series with output at the inductor

• RC series with output at the resistor

Low pass :

• RL series with output at the resistor

• RC series with output at the capacitor

Note: when capacitor (H = haut/high) is standing/ when inductor (L = low or B = bas) is laying

What are the circuit configuration and the phasor diagram of the RL series high pass?

What’s the transfer function of the RL series high pass?

What’s the cutoff frequency? (Definition)

• The frequency at which the ohmic resistance just equals the value of the impedance (ZL or Zc)

• Separates a range in which the filter allows the signal to go through, from one in which it is blocked

• At $fc$ :

  • phase $\varphi=45^{o}$

  • Amplitude $A=\frac{1}{\sqrt2}$

What’s the cutoff frequency for RL series circuits? (Formula)

In the RL series high pass:

What happens at low frequencies for the amplitude response and the phase response?

At high frequencies?

At cutoff frequency?

Sketch the amplitude response and the phase response of the RL high-pass

What are the circuit configuration and the phasor diagram of the RL series low pass?

What’s the transfer function of the RL series low pass?

In the RL series low pass:

What happens at low frequencies for the amplitude response and the phase response?

At high frequencies?

At cutoff frequency?

Sketch the amplitude response and the phase response of the RL low-pass

What’s an RC series circuit?

A circuit with a resistor and a capacitor in series

Sketch the amplitude response and the phase response of the RL low-pass

What’s the transfer function of the RC high-pass?

In the RC series high pass:

What happens at low frequencies for the amplitude response and the phase response?

At high frequencies?

At cutoff frequency?

Sketch the amplitude response and the phase response of the RC high-pass

What’s the cutoff frequency of an RC series circuit? (Formula)

What are the circuit configuration and the phasor diagram of the RC low-pass?

What’s the transfer function of the RC low-pass?

In the RC series low pass:

What happens at low frequencies for the amplitude response and the phase response?

At high frequencies?

At cutoff frequency?

Sketch the amplitude response and the phasor response of the RC low-pass

What’s a series resonant circuit?

What can we say about its output voltage? What should we must do then?

• circuit with a resistor, an inductor and a capacitor in series

• The output voltage is not clearly defined —> we must consider all voltages across each individual component

What’s the relationship between the input voltage and the other components voltages in the RLC circuit?

Using the KVL…

What’s the magnitude the input voltage in the RLC circuit?

How do we find it?

Using the phasor diagram…

What’s the total impedance? (Not complex!)

The magnitude of the total complex impedance…

What’s the phase in the RLC circuit?

What’s the resonance frequency of the RLC circuit? (Definition & properties)

• frequency at which $U_{L}=U_{C}$ and $Z_{L}=Z_{C}$ (NOT L = C !!)

• Total impedance is minimal and purely ohmic

• $U_{L}$ and $U_{C}$ are minimal

• $I$ is maximal

What’s the resonances frequency in the RLC circuit? (Formula)

In the RLC circuit :

What happens at low frequencies?

At resonance frequency?

At low frequencies?

How do the voltages across the resistor, the inductor and the capacitor behave with low, resonance, and high frequency?

What’s the quality factor or Q-factor? (Definition + formula)

• A factor that defines the deviation from the input voltage of the voltage across the capacitor or inductor at resonance

• No unit

• Can be :

  • < 1

  • > 1

  • = 1

What’s ds? (Definition + formula)

• the reciprocal value of the quality factor

• Called the attenuation

Sketch the amplitude response and the phase response of the RLC circuit. Explain the 2 graphs