| Impedance, Z = | V |
| I |
| Resistance, R = | V |
| I |
I = current in amps (A)
Z = impedance in ohms (
)
R = resistance in ohms (
)
Next Page: 555 and 556 Timer Circuits
Also See: Capacitance | Resistance |
Ohm's Law | Voltage Dividers
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| V = voltage in volts (V) I = current in amps (A) Z = impedance in ohms ( )
R = resistance in ohms ( ) |
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Impedance is more complex than resistance because the effects of capacitance and inductance vary with the frequency of the current passing through the circuit and this means impedance varies with frequency! The effect of resistance is constant regardless of frequency.
The term 'impedance' is often used (quite correctly) for simple circuits which have no capacitance or inductance - for example to refer to their 'input impedance' or 'output impedance'. This can seem confusing if you are learning electronics, but for these simple circuits you can assume that it is just another word for resistance.
Four electrical quantities determine the impedance (Z) of a circuit:
resistance (R), capacitance (C),
inductance (L) and frequency (f).
Impedance can be split into two parts:
The capacitance and inductance cause a phase shift* between
the current and voltage which means that the resistance and
reactance cannot be simply added up to give impedance.
Instead they must be added as vectors
with reactance at right angles to resistance as shown in the diagram.
* Phase shift means that the current and voltage are out of step with each other.
Think of charging a capacitor.
When the voltage across the capacitor is zero, the current is at a maximum;
when the capacitor has charged and the voltage is at a maximum, the current is at a minimum.
The charging and discharging occur continually with AC and the current reaches its maximum shortly
before the voltage reaches its maximum: so we say the current leads the voltage.
.
There are two types of reactance: capacitive reactance (Xc) and inductive reactance (XL).
The total reactance (X) is the difference between the two: X = XL - Xc
| Xc = | 1 | where: | Xc = reactance in ohms ()
f = frequency in hertz (Hz) C = capacitance in farads (F) |
2 fC |
For example: a 1µF capacitor has a reactance of
3.2k for a 50Hz signal,
but when the frequency is higher at 10kHz its reactance is only
16.
| XL = 2fL |
where: | XL = reactance in ohms ()
f = frequency in hertz (Hz) L = inductance in henrys (H) |
For example: a 1mH inductor has a reactance of only
0.3 for a 50Hz signal,
but when the frequency is higher at 10kHz its reactance is
63.
Input impedance (ZIN) is the impedance 'seen' by anything connected to the input
of a circuit or device (such as an amplifer). It is the combined effect of all the resistance,
capacitance and inductance connected to the input inside the circuit or device.
It is normal to use the term 'input impedance' even for simple cases where there is only resistance and the term 'input resistance' could be used instead. In fact it is usually reasonable to assume that an input impedance is just resistance providing the input signal has a low frequency (less than 1kHz say).
The effects of capacitance and inductance vary with frequency, so if these are present the input impedance will vary with frequency. The effects of capacitance and inductance are generally most significant at high frequencies.
Usually input impedances should be high, at least ten times the output impedance
of the circuit (or component) supplying a signal to the input. This ensures that the input will not 'overload'
the source of the signal and reduce the strength (voltage) of the signal by a substantial amount.
 |
| The equivalent circuit of any output
|
It is normal to use the term 'output impedance' even for simple cases where there is only resistance and the term 'output resistance' could be used instead. In fact it is usually reasonable to assume that an output impedance is just resistance providing the output signal has a low frequency (less than 1kHz say).
The effects of capacitance and inductance vary with frequency, so if these are present the output impedance
will vary with frequency. The effects of capacitance and inductance are generally most significant at high
frequencies.
Usually output impedances should be low, less than a tenth of the load impedance
connected to the output. If an output impedance is too high it will be unable to supply a sufficiently strong
signal to the load because most of the signal's voltage will be 'lost' inside the circuit driving current through
the output impedance ZOUT.
The load could be a single component or the input impedance of another circuit.
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| The load can be a single component or the input impedance of another circuit
|
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| Voltage divider |
 |
| Equivalent circuit of a voltage divider |
 |
| Voltage divider with an LDR |
For successful use the output impedance of the voltage divider should be much smaller than the input impedance of the circuit it is connected to. Ideally the output impedance should be less than a tenth of the input impedance.
In the equivalent circuit of a voltage divider the output impedance is just a resistance and the term 'output resistance' could be used. ROUT is equal to the two resistances (R1 and R2) connected in parallel:
| Output impedance, ROUT = | R1 × R2 | |
| R1 + R2 |
The voltage source VSOURCE in the equivalent circuit is the value of the output voltage Vo when there is nothing connected to the output (and therefore no output current). It is sometimes called the 'open circuit' voltage.
| Voltage source, VSOURCE = | Vs × R2 | |
| R1 + R2 |
In most voltage dividers one of the resistors will be an input transducer such as an LDR. The transducer's resistance varies and this will make both VSOURCE and ROUT vary too. To check that ROUT is sufficiently low you should work out its highest value which will occur when the transducer has its maximum resistance (this applies wherever the transducer is connected in the voltage divider).
For example: If R1 = 10k
and R2 is an LDR with maximum resistance
1M,
ROUT = 10k × 1M / (10k + 1M)
= 9.9k
(say 10k).
This means it should be connected to a load or input resistance of at least
100k.
