PARALLEL L/C/R CIRCUITS

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4.10 PARALLEL L/C/R CIRCUITS

The effects of connecting these three components in series was studied in the previous section, they can however be connected in parallel. This section studies the effects of connecting the three components in parallel.

4.10.1 INDUCTANCE AND CAPACITANCE IN PARALLEL

As with the series circuit, changes of frequency will again effect the inductive reactance and the capacitive reactance and there will again be one particular frequency at which the two will be equal for a given capacitor and inductor. This is the resonant frequency of the circuit. The formula for this is the same as for the series circuit, providing that the resistive element of the circuit is small. At resonant frequency, the current circulating between the capacitor and the

inductor is high, but the current drawn from the supply is low. This type of circuit is therefore commonly known as a ‘rejector circuit’.

The best way of understanding its operation is to imagine a capacitor and an inductor connect as shown in the diagram.

Imagine also that the capacitor is charged to a given voltage and that there is no resistance in the circuit. When the switch is closed, the capacitor will discharge through the inductor, transferring energy to it. The inductor field will then

collapse, charging the capacitor up in the reverse direction. This action will repeat itself ad infinitum and the current will continue to circulate backwards and forwards at a natural frequency which, of course, is the resonant frequency of the circuit. This ideal condition would need no external force to keep operating.

In practice, however, there must be some resistance in our circuit and so the current will oscillate at resonant frequency, but will gradually die away as power is

JAR 66 CATEGORY B1 MODULE 3 (part B)

ELECTRICAL FUNDAMENTALS

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If a graph is drawn of supply current (or line current, as it is sometimes known) against frequency, the result will be as shown below.

The very high impedance at resonance associated with parallel circuits is most often used in the tuning circuits of radio or television receivers. When tuned to a particular frequency, that frequency will not pass through the parallel circuit. It is therefore available for the amplifier to amplify and use. All the other (unwanted) frequencies coming in at the aerial are passed through the parallel circuit to the chassis, thereby by-passing the amplifier.

At frequencies above resonance, the circuit acts as though it were capacitive and at frequencies below resonance, as though it were inductive.

4.10.2 PARALLEL RESONANCE

Unlike the series tuned circuit, the resistance does have an effect on the resonant frequency of a parallel tuned circuit, the equation being:

fo = 1

2 1 LC - R²

L²

JAR 66 CATEGORY B1 MODULE 3 (part B)

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At resonance, the supply current (IS) is a minimum and is in phase with the applied voltage. The value of the resonant current, as shown in the diagram below, is given by Vs

ZD or VsCR L

In a Parallel Circuit at Resonant Frequency (fO):

XL = XC

VL = VC and are in antiphase and therefore cancel each other out VR = Applied Voltage V.

Z = L

CR and current is a minimum.

Because the impedance is a maximum, the parallel resonant circuit is known as a ‘rejecter circuit’.

4.10.3 IMPEDANCE

The impedance of a parallel circuit can be calculated using the formula shown below, although knowledge of this formula is not essential on this course.

2 2

1 1 1

1

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4.10.4 CURRENT MAGNIFICATION

In a parallel tuned circuit at resonance, current magnification occurs, that is IL and IC will be very large compared with IS. At any instant IL and IC act in the same direction round the ‘internal’ circuit, and IS flowing in the ‘external’ circuit is the difference between IL and IC. Thus, if IL and IC are large and very nearly equal, IS

will be small.

At any instant Kirchoff’s first law applies, that is:

IS = IL + LC

The circulating current is the smaller of the two currents (IL or IC) and IS is the make-up current.

Remember that QO for a series tuned circuit is its voltage magnification whereas QO for a parallel tuned circuit is its current magnification at the resonant

frequency.

Bandwidth is defined as the difference between two frequencies f1 and f2, one either side of resonance, at which the impedance has fallen to 0.707 of the maximum value.

As for the series circuit:

Bandwidth B = fO

C decreased, then the impedance at resonance is decreased, QO is decreased and hence bandwidth increased.

JAR 66 CATEGORY B1 MODULE 3 (part B)

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4.10.6 SELECTIVITY

As for the series circuit, selectivity is the ability of the tuned circuit to respond strongly to its resonant frequency and to give a poor response to nearby frequencies. Again, as for the series circuit, QO is used as a measure of selectivity.

Below fO Above fO

1. Z small due to small XL

1. Z small due to small XC

2. XC > XL 2. XL > XC

3. Thus IL > IC 3. Thus IC > IL

4. Thus circuit inductive 4. Thus circuit capacitive

JAR 66 CATEGORY B1 MODULE 3 (part B)

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5 TRANSFORMERS

Transformers have no moving parts and are very efficient pieces of electrical equipment. Transformers operate by mutual inductance, the flux from one coil of wire linking with another coil. Because the flux must be changing state, static transformers can only be used on alternating current. In order for a transformer to be used on direct current, part of the transformer must be rotated.