Emitter Resistance

Table of Contents

The aim of an AC signal amplifier circuit is to stabilise the DC biased input voltage to the amplifier and thus only amplify the required AC signal.

This stabilisation is achieved by the use of an Emitter Resistance which provides the required amount of automatic biasing needed for a common emitter amplifier. To explain this a little further, consider the following basic amplifier circuit below.

Basic Common Emitter Amplifier Circuit

common emitter amplifier circuit

The common emitter amplifier circuit shown uses a voltage divider network to bias the transistors base and the common emitter configuration is a very popular way of designing bipolar transistor amplifier circuits. An important feature of this circuit is that an appreciable amount of current flows into the base of the transistor.

The voltage at the junction of the two biasing resistors, R1 and R2, holds the transistors base voltage, VB at a constant voltage and proportional to the supply voltage, Vcc. Note that VB is the voltage measured from base to ground, which is the actual voltage drop across R2.

This “class-A” type amplifier circuit is always designed so that the base current ( Ib ) is less than 10% of the current flowing through the biasing resistor R2. So for example, if we require a quiescent collector current of 1mΑ, the base current, IB will be about one hundredth of this, or 10μΑ. Therefore the current flowing through resistor R2 of the potential divider network must be at least 10 times this amount, or 100μΑ.

The advantage of using a voltage divider lies in its stability. Since the voltage divider formed by R1 and R2 is lightly loaded, the base voltage, Vb can be easily calculated by using the simple voltage divider formula as shown.

Voltage Divider Equation

voltage divider equation

However, with this type of biasing arrangement the voltage divider network is not loaded by the base current as it is too small, so if there are any changes in the supply voltage Vcc, then the voltage level on the base will also change by a proportional amount. Then some form of voltage stabilisation of the transistors base bias or Q-point is required.

Emitter Resistance Stabilisation

emitter resistance

The amplifiers bias voltage can be stabilised by placing a single resistor in the transistors emitter circuit as shown. This resistance is known as the Emitter ResistanceRE. The addition of this emitter resistor means that the transistors emitter terminal is no longer grounded or at zero volt potential but sits at a small potential above it given by the Ohms Law equation of: VE = IE x RE. Where: IE is the actual emitter current.

Now if the supply voltage Vcc increases, the transistors collector current Ic also increases for a given load resistance. If the collector current increases, the corresponding emitter current must also increase causing the voltage drop across RE to increase. This action results in a proportional increase in base voltage because VB = VE + VBE

Since the base voltage is held constant by the divider resistors R1 and R2, the DC voltage on the base relative to the emitter Vbe is lowered by a proportional amount thus reducing the base current drive and keeping the collector current from increasing further. A similar action occurs if the supply voltage and collector current try to decrease in value.

In other words, the addition of this emitter terminal resistance helps control the transistors base biasing using negative feedback, which negates any attempted change in collector current with an opposing change in the base bias voltage and so the circuit tends to be stabilised at a fixed level.

Also, since part of the supply is dropped across RE, its value should be as small as possible so that the largest possible voltage can be developed across the load resistance, RL and therefore the output. However, its value cannot be too small or once again the instability of the circuit will suffer.

Then the current flowing through the emitter resistor is calculated as:

Emitter Resistor Current

emitter resistor current

As a general rule of thumb, the voltage drop across this emitter resistance is generally taken to be: VB – VBE, or one-tenth (1/10th) of the value of the supply voltage, Vcc. A common figure for the emitter resistor voltage is between 1 to 2 volts, whichever is the lower. The value of the emitter resistance, RE can also be found from the gain as now the AC voltage gain is equal to: RL / RE

Emitter Resistance Example No1

A common emitter amplifier has the following characteristics, β = 100Vcc = 30V and RL = 1kΩ. If the amplifier circuit uses an emitter resistance to improve its stability, calculate its resistance.

The amplifiers quiescent current, ICQ is given as:

amplifier currents

The voltage drop across the emitter resistance is generally between 1 and 2 volts, so lets assume a voltage drop, VE of 1.5 volts.

emitter resistance equation

Then the value of the Emitter Resistance required for the amplifier circuit is given as: 100Ω, and the final common emitter circuit is given as:

Final Common Emitter Amplifier

common emitter amplifier

The gain of the amplifier stage can also be found if so required and is given as:

common emitter amplifier gain

Emitter By-pass Capacitor

In the basic series feedback circuit above, the emitter resistor, RE performs two functions: DC negative feedback for stable biasing and AC negative feedback for signal transconductance and voltage gain specification. But as the emitter resistance is a feedback resistor, it will also reduce the amplifiers gain due to fluctuations in the emitter current IE owing to the AC input signal.

emitter bypass capacitor circuit

To overcome this problem a capacitor, called an “Emitter Bypass Capacitor”, CE is connected across the emitter resistance as shown. This bypass capacitor causes the frequency response of the amplifier to break at a designated cut-off frequency, ƒc, by-passing (hence its name) signal currents to ground.

Being a capacitor it appears as an open circuit for the for DC bias and therefore, the biased currents and voltages are unaffected by the addition of the bypass capacitor. Over the amplifiers operating range of frequencies, the capacitors reactance, XC will be extremely high at low frequencies producing a negative feedback effect, reducing the amplifiers gain.

The value of this bypass capacitor CE is generally chosen to provide a capacitive reactance of, at most one-tenth (1/10th) of the value of the emitter resistor RE at the lowest cut-off frequency point. Then assuming that the lowest signal frequency to be amplified is 100 Hz. The value of the bypass capacitor CE is calculated as:

Emitter Bypass Capacitor

emitter bypass capacitor equation

Then for our simple common emitter amplifier above the value of the emitter bypass capacitor connected in parallel with the emitter resistance is: 160μF

Split Emitter Amplifier

While the addition of the bypass capacitor, CE helps to control the amplifiers gain by counteracting the effects of the uncertainty of beta, ( β ), one of its main disadvantages is that at high frequencies the capacitors reactance becomes so low that it effectively shorts out the emitter resistance, RE as the frequency increases.

The result is that at high frequencies the reactance of the capacitor allows very little AC feedback control because RE is shorted out which also means that the AC voltage gain of the transistor is greatly increased driving the amplifier into saturation.

One easy way of controlling the amplifiers gain over the whole operating frequency range is to split the emitter resistance into two parts as shown.

Split Emitter Resistors

split emitter resistors

The resistor in the emitter leg has been split into two parts: RE1 and RE2 forming a voltage divider network within the emitter leg with the by-pass capacitor connected in parallel across the lower resistor.

The upper resistor, RE1 is the same value as before but is unbypassed by the capacitor so must be considered when calculating signal parameters. The lower resistor RE2 is connected in parallel with the capacitor and is considered to be zero ohms when calculating signal parameters as it becomes shorted out at high frequencies.

The advantage here is that we can control the AC gain of the amplifier over the full range of input frequencies. At DC the total value of the emitter resistance is equal to RE1 + RE2 while at higher AC frequencies the emitter resistance is just: RE1, the same as it was in the original unbypassed circuit above.

So what value is resistor, RE2. Well that will depend upon the DC voltage gain required at the lower frequency cut-off point. We said earlier that the gain of the above circuit was equal to: RL / RE which for our common emitter circuit above was calculated at 10 (1kΩ/100Ω). But now at DC the gain will be equal to: RL / (RE1 + RE2)

Therefore if we choose a DC gain of say 1 (one) the value of emitter resistor, RE2 is given as:

Split-emitter Resistor, RE2

split emitter resistor re2

Then for a DC gain of 1 (one), RE1 = 100Ω and RE2 = 900Ω. Note that the AC gain will be the same at 10.

Then a split-emitter amplifier has values of voltage gain and input impedance somewhere between those of a fully bypassed emitter amplifier and an unbypassed emitter amplifier depending upon the operating frequency.

Emitter Resistance Summary

Then to summarise, the current amplification parameter, β of a transistor can vary considerably from one device to another of the same type and part number because of manufacturing tolerances, and also due to variations in supply voltage and operating temperature.

Then for a common emitter class-A amplifier circuit it is necessary to use a biasing circuit that will stabilize the operating Q-point making the DC collector current, IC independent of beta. The influence of β on the value of the emitter current can be reduced by the addition of an Emitter ResistanceRE in the emitter leg to provide stabilisation.

The voltage drop across this emitter resistance is usually given as between 1 to 2 volts. The emitter resistor can be fully bypassed by a suitable bypass capacitor, CE connected in parallel with the emitter resistor to achieve a higher AC gain or partly bypassed, using a split-emitter voltage divider network which reduces the DC gain and distortion. The value of this capacitor is determined from its capacitive reactance (XC) value at the lowest signal frequency.


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