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There is a 180 degree phase difference between the two components (thus they can cancel each other out during resonance).
The resistor R represents the imperfections in L and C (preventing resonance from going to infinity).
[image] |
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The Q factor is the ratio of the reactance to the resistance R and is the same for the whole circuit (individual components can have their own which is then represented as its own resistor):
[image]
Therefore, at resonance: [image] |
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The two values where the peak voltage is reduced by a factor of roo(2) create the bandwidth.
[image]
(For large values of Q - bigger than 10)
'Half-power bandwidth' is is the range of frequencies over which the power in the circuit is at least half of its maximum value. So just the bandwidth.
In the formula booklet dw is actually the frequency offset which is the distance the circuit is working at from resonance (w - w0). It can be half the bandwidth (i.e from angular resonant frequency to one of the points where it crosses [image], so for full bandwidth just ignore the 1/2). Z is impedance and Y is admittance (1/Z). |
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| LC resonant circuit when the inductor is in parallel |
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| Two port models: the amplifier model |
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| Gain graph of the amplifier |
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[image]
The earlier model has linear gain, but some gains can be a function of frequency. |
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| How does the amplifier work when connected to other circuit elements? |
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| Power through the amplifier |
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[image]
This is for a circuit that has no Rs, if there is an Rs, [image]. |
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| How to maximise the power transfer through the amplifier? |
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[image]
Therefore, for maximum power the load and output impedance should be matched. |
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| How does the amplifier increase the power? |
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There is a power supplied through positive and negative supply rails.
[image]
Hence, these power supplies set the maximum and minimum voltage swing in the output. If the gain is too high, the voltage will be clipped.
[image] |
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| How to find out the output impedance? |
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By short circuiting the input, (often, not always) only the output circuit can be measured. A test voltage is applied to the output Vx and the test current ix is measure.
[image] |
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| Frequency response of the amplifier circuit (lower frequencies and circuit diagram) |
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| Frequency response of the amplifier circuit (higher frequencies and frequency graph) |
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