A bipolar junction transistor, (BJT) is very versatile. It can be used in many ways, as an amplifier, a switch or an oscillator and many other uses too. Before an input signal is applied its operating conditions need to be set. This is achieved with a suitable bias circuit, some of which I will describe. A bias circuit allows the operating conditions of a transistor to be defined, so that it will operate over a pre-determined range. This is normally achieved by applying a small fixed dc voltage to the input terminals of a transistor.

Bias design can take a mathematical approach or can be simplified using transistor characteristic curves. The characteristic curves predict the performance of a BJT. There are three curves, an input characteristic curve, a transfer characteristic curve and an output characteristic curve. Of these curves, the most useful for amplifier design is the output characteristics curve. The output characteristic curves for a BJT are a graph displaying the output voltages and currents for different input currents. The linear (straight) part of the curve needs is utilized for an amplifier or oscillator. For use as a switch,a transistor is biased at the extremities of the graph, these conditions are known as "cut-off" and "saturation".

Output Characteristic CurvesFor each transistor configuration, common emitter, common base and emitter follower the output curves are slightly different. A typical output characteristic for a BJT in common emitter mode are shown below :-

After the initial bend, the curves approximate a straight line. The slope or gradient of each line represents the output impedance, for a particular input base current. So what has all this got to do with biasing ? Take, for example the middle curve. The collector emitter voltage is displayed up to 20 volts. Let's assume that we have a single stage amplifier, working in common emitter mode, and the supply voltage is 10 volts. The output terminal is the collector, the input is the base, where do you set the bias conditions? The answer is anywhere on the flat part of the graph. However, imagine the bias is set so that the collector voltage is 2 volts. What happens if the output signal is 4 volts peak to peak ? Depending on whether the transistor used is a PNP or NPN, then one half cycle will be amplified cleanly, the other cycle

will approach the limits of the power supply and will "clip". This is shown below :

The above diagram shows a 4 volt peak to peak waveform with clipping on the positive half cycle. This is caused by setting the bias at a value other than half the supply voltage.

The lower diagram shows the same amplifier, but here the bias is set so that collector voltage is half the value of the supply voltage. Hence, it is a good idea to set the bias for a single stage amplifier to half the supply voltage, as this allows maximum output voltage swing in both directions of an output waveform.

Input Characteristic Curves

Before describing the bias circuits, it is worthwhile looking at a typical input characteristic curve for a small signal BJT, shown left. The input characteristics for a transistor in common emitter mode is a plot of input base emitter voltage (x-axis) verses base current (y-axis). The graph is drawn with both x and y axis slightly zoomed.

The base emitter voltage, Vbe, for a small signal transistor is typically quoted in many text books as either 0.6 V or 0.7 V Both values are an approximation,and as can be seen from the graph the value of Vbe varies with collector current, device type and temperature. With low base currents of 50uA or less, taking Vbe as 0.6 volts is a reasonable approximation. For higher base currents, and in switching circuits using Vbe as 0.7 V is a better

approximation. In large power transistors, Vbe can be even and often be as high as 0.8 or 0.9V.

Simple Bias CircuitThe simplest bias circuit is shown below. It consists only of a fixed bias resistor and load resistor. The BJT is operating in common emitter mode. The dc current gain or beta, hFE is the ratio of dc collector current divided by dc base current. The BJT is a BC107A. The values of Rb and Rc can be determined by either mathematical approach or by using the output characteristic curves for the BC107A.

Quiescent Point (Q-Point)The point Vo in the diagram above is where the output signal would be taken. For simplicity,the input signal and coupling capacitors have been omitted. For minimum distortion and clipping it is desirable to bias this point to half the supply voltage, 10 volts dc in this case. This is also known as the quiescent point. The ac

output signal would then be superimposed on the dc bias voltage.The Q-point is sometimes indicated on the output characteristics curves for a transistor amplifier. The quiescent point also refers to the dc conditions (bias conditions) of a circuit without an input signal.

Q-Point ValueI have mentioned that setting the Q-point to half the supply voltage is a good idea. It gives a circuit the highest margin for overload. However, any amplifier will clip if the input amplitude exceeds the limit for which the circuit was designed. However, there are certain cases when it is not necessary to bias a stage to half the supply voltage. Examples would be an RF amplifier design where the input signal is in microvolts or millivolts. If the stage had a gain of 200 then the output (assuming a 2mV peak input) would only need to swing up and down 400mV about the Q-point. Hence a stage with a supply voltage of 12 volts could have its Q-point set at 10 volts or even 2 volts without problems. Another example would be a microphone stage where similar low level input signals are involved.

Output Characteristic Curve for a BC107AClick on the graph to zoom in (full screen display)

Bias Design:The collector voltage Vc for the simple bias design is 10 volt. The dc current gain, hFE for the BC107A is obtained from the manufacturers data sheets and varies between devices. A typical beta is around 290. Taking a base current of 20uA and reading values direct from the output curves, the collector current, for a collector emitter voltage of 10 volts is around 3.9mA. As hFE= Ic / Ib then a BC107A must have a beta of at least 3.9mA / 20uA = 195 to work with this circuit. Also, the base emitter voltage, Vbe is typically 0.6v. Knowing the above data and using ohm's law , values for Rb and Rc can be determined:

Rb = Vcc - Vbe / Ib = (20-0.6) / 20u = 970k use (1M)

Rc = Vc / Ic = 10 / 3.9m = 2.56K use (2.7K)

Mathematical Approach:Without using the output characteristic curve, values for Rb and Rc can still be calculated. A value for hFE must be estimated first and a desired collector current. As hFE varies in each transistor the value chosen should be the lowest value from the manufacturers data sheets. he equations to use are:

Rc = Vc / Ic

Ib = Ic / hFE

Rb = Vcc - 0.6 / Ib.

Using the example above with Vcc=20 and hFE =195 yields the same values.

Temperature StabilityThe above circuit is not good for the following reasons. It relies heavily on a transistor with a current gain very close to 195. Other samples will give different results. Variations in the supply voltage produce changes in the quiescent values, and also a change in temperature will alter the current gain of the transistor and hence quiescent point. For use as an amplifier this could mean distortion of the output signal above a certain temperature. The graph below displays the collector voltage and current for the simple bias circuit over a temperature range of -50 to +50 degrees Celsius.

As can be seen both Vq and Iq will vary over a wide range. This is the reason that this circuit is seldom used. It is clear that a different circuit arrangement is needed.

Self Stabilizing BiasCoupling capacitors have been omitted for clarity, the output is taken from the transistor collector :

This is similar to the self bias circuit with one difference: the base resistor Rb is returned to the transistor collector instead of the supply voltage. The reason for this is simple; if the transistor used had a high current gain, then the collector voltage would fall. As Rb is connected to the collector then the base current would be reduced to counter the effect. If the transistor had a low value of beta, then the collector voltage would rise. This in turn provides more base current for the transistor to conduct harder and stabilize the q-point. The equations to calculate Rc and Rb follow:-

Rc = Vc / Ic

Rb = Vc - Vbe / Ib

as Ib = Ic / hFE then

Rb = (Vc -Vbe) * hFE/ Ic

Self stabilizing bias example:A bias circuit is required to bias a transistor to half the

supply voltage. A BC107A transistor with hfe of 200 is used and supply voltage, Vcc is 20 volts. The collector current is to be 1mA. The resistor values are:

Rc = Vc / Ic = 10 / 1mA = 10K

Rb = (Vc-Vbe)*hFE / Ic = (10-0.6)*200 /1mA = 1880k a 1.8M resistor is fine here.

Temperature Stability of Self Stabilizing Bias CircuitThis method of biasing is more resilient to changes of temperature as shown in the graph below. It is unlikely that anything you make will be tested under this extreme range of temperatures, however some parts of the world, for example Mongolia have Winters where temperatures plumit to -40° C and Summers that can reach +40° C ! If you live in an extreme climate then the effects of temperature must be taken into consideration. The results below show quiescent collector voltage and currents and can be compared to the simple bias circuit above.

Potential Divider BiasThis is the most widely used biasing scheme in general electronics. For a single stage amplifier this circuit offers the best resilience to temperature changes and variation in device characteristics. The disadvantage is that a couple of extra resistors are required, but this is outweighed by the advantage of excellent stability. The circuit is shown below:

Here R1 and R2 form a potential divider, which will fix the base potential of the transistor. The current through this bias chain is usually set at 10 times greater than the base current required by the transistor. The base emitter voltage drop of the transistor is approximated as 0.6 volt. There will also be a voltage drop across the emitter resistor, Re, this is generally set to about 10% of the supply voltage. The inclusion of this resistor also helps to stabilize the bias: If the temperature increases, then extra collector current will flow. If Ic increases, then so will Ie as Ie= Ib + Ic. The extra current flow through Re increases the voltage drop across this resistor reducing the effective base emitter voltage and therefore stabilizing the collector current. The equations follow:

Rc = Vc / Ic

Ie = Ib + Ic as Ic >> Ib then Ie ~ Ic

Ve = 10% * Vcc

Re= Ve / Ie

Vb = Ve + 0.6

R2 = Vb / 10 * Ib

R1 = Vcc-Vb / 10 * Ib

An Example:Using the values of the previous examples a direct comparison of stability can be demonstrated. The values are;Vcc=20V, Vc=10V, Ic = 1mA, transistor is BC107A with hFE=195

Rc= Vc /Ic = 10 / 1m = 10k

Ve = 10% * 20 = 2V

Re = Ve / Ie= 2 / 1= 2k

Vb = 2+ 0.6 = 2.6V

Ib = Ic / hFE = 1 / 195 =0.005128mA

R2 = Vb / 10* Ib = 2.6 / 0.05128 = 50.7k use 47k

R1 = Vcc-Vb / 10 * Ib = (20-2.6) / 0.05128 = 339.3k use 330k

Using these values and plotting the change in quiescent conditions for Vc and Ic over a temperature range of -50 to +50 celcius is displayed below:

As shown above, this bias circuit offers the best stability against variations in Vc and Ic over a very wide temperature range. As the resistor values used were preferred values, then the quiescent point will be slightly different from the calculated value.

Biasing of a Transistor

Biasing a Transistor amplifier is the process of setting the DC operating voltage and current to the correct level so that any AC input signal can be amplified correctly by the transistor. The correct bias point of the transistor is generally somewhere between the two extremes of operation with respect to it being either “fully-ON” or “fully-OFF” along the load line. This central operating point is called the “Quiescent Operating Point”, or Q-point for short.When a bipolar transistor is biased so that the Q-point is near the middle of its operating range, that is approximately halfway between cutoff and saturation, it is said to be operating as a Class-A amplifier. This mode of operation allows the output current to increase and decrease around the

amplifiers Q-point without distortion as the input signal swings through a complete cycle. In other words, the output current flows for the full 360o of the input cycle.So how do we set this Q-point biasing of a transistor? – The correct biasing of the transistor is achieved using a process know commonly as Base Bias. The function of the “DC Bias level” or “no input signal level” is to correctly set the transistors Q-point by setting its Collector current ( IC ) to a constant and steady state value without an input signal applied to the transistors Base. This steady-state or DC operating point is set by the values of the circuits DC supply voltage ( Vcc ) and the value of the biasing resistors connected the transistors Base terminal.Since the transistors Base bias currents are steady-state DC currents, the appropriate use of coupling and bypass capacitors will help block bias current setup for one transistor stage affecting the bias conditions of the next. Base bias networks can be used for Common-base (CB), common-collector (CC) or common-emitter (CE) transistor configurations. In this simple transistor biasing tutorial we will look at the different biasing arrangements available for a Common Emitter Amplifier.

Base Biasing a Common Emitter Amplifier

One of the most frequently used biasing circuits for a transistor circuit is with the self-bias of the emitter-bias circuit where one or more biasing resistors are used to set up the initial DC values of transistor currents, ( IB ), ( IC ) and ( IE ). This is achieved either using a feed back resistor or by using a simple voltage divider circuit to provide biasing voltage. The following are five examples of transistor Base bias configurations from a single supply ( Vcc ).Current Biasing a Transistor

A two resistor biasing network is used to establish the initial operating region of transistor with a “fixed current bias”. The Emitter diode of the transistor is forward biased by applying the required positive Base bias voltage via the current limiting resistor RB.

Assuming a standard bipolar transistor, the forward Base-emitter voltage drop will be 0.7V. Then the value of IB is simply: (VCC – VBE)/IB. With this type of biasing method the biasing voltages and currents do not remain stable during transistor operation. Feedback Biasing a Transistor

This transistor biasing configuration again requires only two resistors. The Collector feedback configuration ensures that the transistor is always biased in the active region regardless of the value of Beta (β). The Base bias is derived from the Collector voltage.If the Collector current increases, the Collector voltage drops, reducing the Base drive and thereby automatically reducing the Collector current. The transistors stability using this type of bias network is generally good for most amplifier designs.  Dual Feedback Biasing a Transistor

 Adding an additional resistor to the Base bias network of the previous configuration improves stability even more with respect to variations in Beta, (β) by increasing the current flowing through

the Base bias resistors. The current flowing through RB1 is generally set at a value equal to about 10% of Collector current, IC.One of the advantages of this type of biasing configuration is that the resistors provide both biasing and Rf feedback at the same time.    Voltage Divider Biasing a Transistor with Compensation

The common Emitter transistor is biased using a voltage divider network. The name ofthis biasing configuration comes from the fact that the two resistors RB1and RB2 are connected to the transistors Base terminal across the supply. This voltage divider configuration is the most widely used biasing method, as the Emitter diode of the transistor is forward biased by the voltage dropped across resistor RB2.To calculate the voltage developed across resistor RB2 and therefore the voltage applied to the Base terminal we simply use the voltage divider formula. The current flowing through resistor RB2 is generally set at 10 times the value of the required Base current IB so that it has no effect on the voltage divider current.Dual Feedback Biasing a Transistor with Emitter Compensation

 This type of biasing configuration uses both Emitter and Collector-base feedback to stabilize the Collector current. Resistor values are generally set so that the voltage drop across Emitter resistor RE is approximately 10% of VCC and the current flowing through resistor RB1 is 10% of the Collector current IC.This type of transistor biasing configuration works best at relatively low power supply voltages.    The goal of biasing a transistor is to establish a known Q-point in order to work efficiently and produce an undistorted output signal. Correct biasing of the transistor also establishes its initial AC operating region with practical biasing circuits using either a two or four-resistor bias network. In bipolar transistor circuits, the Q-point is represented by (VCE, IC) for the NPN transistors or (VEC, IC) for PNP transistors. The stability of the Base bias network and therefore the Q-point is generally assessed by considering the Collector current as a function of both Beta (β) and temperature.Here we have looked briefly at five different configurations for “biasing a transistor” using resistive networks. But we can also bias a transistor using either silicon diodes, zener diodes or active networks all connected to the Base terminal of the transistor or by biasing it from a dual power supply.

mplifier is a circuit that is used for amplifying a signal. The input

signal to an amplifier will be a current or voltage and the output

will be an amplified version of the input signal. An amplifier

circuit which is purely based on a transistor or transistors is

called a transistor amplifier. Transistors amplifiers are commonly

used in applications like RF (radio frequency), audio, OFC (optic

fibre communication) etc. Anyway the most common application

we see in our day to day life is the usage of transistor as an audio

amplifier. As you know there are three transistor configurations

that are used commonly i.e. common base (CB), common

collector (CC) and common emitter (CE). In common base

configuration has a gain less than unity and common collector

configuration (emitter follower) has a gain almost equal to unity).

Common emitter follower has a gain that is positive and greater

than unity. So, common emitter configuration is most commonly

used in audio amplifier applications.

A good transistor amplifier must have the following parameters;

high input impedance, high band width, high gain, high slew

rate, high linearity, high efficiency, high stability etc. The above

given parameters are explained in the next section.

Input impedance: Input impedance is the impedance seen by the

input voltage source when it is connected to the input of the

transistor amplifier. In order to prevent the transistor amplifier

circuit from loading the input voltage source, the transistor

amplifier circuit must have high input impedance.

Bandwidth.

The range of frequency that an amplifier can amplify properly is

called the bandwidth of that particular amplifier. Usually the

bandwidth is measured based on the half power points i.e. the

points where the output power becomes half the peak output

power in the frequency Vs output graph. In simple words,

bandwidth is the difference between the lower and upper half

power points. The band width of a good audio amplifier must be

from 20 Hz to 20 KHz because that is the frequency range that is

audible to the human ear. The frequency response of a single

stage RC coupled transistor is shown in the figure below (Fig 3).

Points tagged P1 and P2 are the lower and upper half power

points respectively.

RC coupled amplifier frequency response

Gain.

Gain of an amplifier is the ratio of output power to the input

power. It represents how much an amplifier can amplify a given

signal. Gain can be simply expressed in numbers or in decibel

(dB). Gain in number is expressed by the equation G = Pout / Pin.

In decibel the gain is expressed by the equation Gain in dB = 10

log (Pout / Pin). Here Pout is the power output and Pin is the

power input. Gain can be also expressed in terms of output

voltage / input voltage or output current / input current. Voltage

gain in decibel can be expressed using the equation, Av in dB =

20 log ( Vout / Vin) and current gain in dB can be expressed

using the equation Ai = 20 log (Iout / Iin).

Derivation of gain.

G = 10 log ( Pout / Pin)………(1)

Let Pout = Vout / Rout and Pin = Vin / Rin. Where Vout is the

output voltage Vin is the input voltage, Pout is the output power,

Pin is the input power, Rin is the input voltage and Rout is the

output resistance. Substituting this in equation 1 we have

G = 10log ( Vout²/Rout) / (Vin²/Rin)………….(2)

Let Rout = Rin, then the equation 2 becomes

G = 10log ( Vout² / Vin² )

i.e.

G = 20 log ( Vout / Vin )

Efficiency.

Efficiency of an amplifier represents how efficiently the amplifier

utilizes the power supply. In simple words it is a measure of how

much power from the power supply is usefully converted to the

output. Efficiency is usually expressed in percentage and the

equation is  ζ = (Pout/ Ps) x 100. Where ζ is the efficiency,

Pout is the power output and Ps is the power drawn from the

power supply.

Class A transistor amplifiers have up to 25% efficiency, Class AB

has up to 55% can class C has up to 90% efficiency. Class  A

provides excellent signal reproduction but the efficiency is very

low  while Class C has high efficiency but the signal reproduction

is bad. Class AB stands in between them and so it is used

commonly in audio amplifier applications.

Stability.

Stability is the capacity of  an amplifier to resist oscillations.

These oscillations may be high amplitude ones masking the

useful signal or very low amplitude, high frequency oscillations

in the spectrum. Usually stability problems occur during high

frequency operations, close to 20KHz in case of audio amplifiers.

Adding a Zobel network at the output, providing negative

feedback etc improves the stability.

Slew rate.

Slew rate of an amplifier  is the maximum rate of change of

output per unit time. It represents how quickly the output of an

amplifier can change in response to the input. In simple words, it

represents the speed of an amplifier. Slew rate is usually

represented in V/μS and the equation is  SR = dVo/dt.

Linearity.

An amplifier is said to be linear if there is a linear relationship

between the input power and the output power. It represents the

flatness of the gain. 100% linearity is not possible practically as

the amplifiers using active devices like BJTs , JFETs or MOSFETs

tend to lose gain at high frequencies due to internal parasitic

capacitance. In addition to this the input DC decoupling

capacitors (seen in almost all practical audio amplifier circuits)

sets a lower cutoff frequency.

Noise.

Noise refers to unwanted and random disturbances in a signal. In

simple words, it can be said to be unwanted fluctuation or

frequencies present in a signal. It may be due to design flaws,

component failures, external interference, due to the interaction

of two or more signals present in a system, or by virtue of certain

components used in the circuit.

Output voltage swing.

Output voltage swing is the maximum range up to which the

output of an amplifier could swing. It is measured between the

positive peak and negative peak and in  single supply amplifiers

it is measured from positive peak to the ground. It usually

depends on the factors like supply voltage, biasing, and

component rating.Common emitter RC coupled amplifier.The common emitter RC coupled amplifier is one of the simplest

and elementary transistor amplifier that can be made. Don’t

expect much boom from this little circuit, the main purpose of

this circuit is pre-amplification i.e to make weak signals strong

enough for further processing or amplification. If designed

properly, this amplifier can provide excellent signal

characteristics. The circuit diagram of a single stage common

emitter RC coupled amplifier using transistor is shown in Fig1.

RC coupled amplifier

Capacitor Cin is the input DC decoupling capacitor which blocks

any DC component if present in the input signal from reaching

the Q1 base. If any external DC voltage reaches the base of Q1, it

will alter the biasing conditions and affects the performance of

the amplifier.

R1 and R2 are the biasing resistors. This network provides the

transistor Q1′s base with the necessary bias voltage to drive it

into the active region. The region of operation where the

transistor is completely switched of is called cut-off region and

the region of operation where the transistor is completely

switched ON (like a closed switch) is called saturation region.

The region in between cut-off and saturation is called active

region. Refer Fig 2 for better understanding. For a transistor

amplifier to function properly, it should operate in the active

region. Let us consider this simple situation where there is no

biasing for the transistor. As we all know, a silicon transistor

requires 0.7 volts for switch ON and surely this 0.7 V will be

taken from the input audio signal by the transistor. So all parts of

there input wave form with amplitude ≤ 0.7V will be absent in

the output waveform. In the other hand if the transistor is given

with a heavy bias at the base ,it will enter into saturation (fully

ON) and behaves like a closed switch so that any further change

in the base current due to the input audio signal will not cause

any change in the output. The voltage across collector and

emitter will be 0.2V at this condition (Vce sat = 0.2V). That is

why proper biasing is required for the proper operation of a

transistor amplifier.

BJT output characteristics

Cout is the output DC decoupling capacitor. It prevents any DC

voltage from entering into the succeeding stage from the present

stage. If this capacitor is not used the output of the amplifier

(Vout) will be clamped by the DC level present at the transistors

collector.

Rc is the collector resistor and Re is the emitter resistor. Values

of Rc and Re are so selected that 50% of Vcc gets dropped across

the collector & emitter of the transistor.This is done to ensure

that the operating point is positioned at the center of the load

line. 40%  of Vcc is dropped across Rc and 10% of Vcc is dropped

across Re. A higher voltage drop across Re will reduce the

output voltage swing and so  it is a common practice to keep the

voltage drop across Re = 10%Vcc . Ce is the emitter by-pass

capacitor. At zero signal condition (i.e, no input) only

the quiescent current (set by the biasing resistors R1 and R2

flows through the Re). This current is a direct current of

magnitude few milli amperes and Ce does nothing. When input

signal is applied, the transistor amplifies it and as a result a

corresponding alternating current flows through the Re. The job

of  Ce is to bypass this alternating component of  the emitter

current. If Ce is not there , the entire emitter current will flow

through Re and that causes a large voltage drop across it. This

voltage drop gets added to the Vbe of the transistor and the bias

settings will be altered. It reality, it is just like giving a heavy

negative  feedback and so it drastically reduces the gain.Design of RC coupled amplifier.The design of a single stage RC coupled amplifier is shown

below.

The nominal vale of collector current Ic and hfe can be obtained

from the datasheet of the transistor.

Design of Re and Ce.

Let voltage across Re; VRe = 10%Vcc ………….(1)

Voltage across Rc; VRc = 40% Vcc. ……………..(2)

The remaining 50% will drop across the collector-emitter .

From (1) and (2)  Rc =0.4 (Vcc/Ic)  and Re = 01(Vcc/Ic).

Design of R1 and R2.

Base current Ib = Ic/hfe.

Let Ic ≈ Ie .

Let current through R1; IR1  = 10Ib.

Also voltage across R2 ; VR2 must be equal to Vbe + VRe. From

this VR2 can be found.

There fore VR1 = Vcc-VR2. Since VR1 ,VR2 and IR1 are found we

can find R1 and R2 using the following equations.

R1 = VR1/IR1 and R2 = VR2/IR1. 

Finding Ce.

Impedance of emitter by-pass capacitor should be one by tenth of

Re.

i.e, XCe = 1/10 (Re) .

Also XCe = 1/2∏FCe.

F can be selected to be 100Hz.

From this Ce can be found.

Finding Cin.

Impedance of the input capacitor(Cin) should be one by tenth of

the transistors input impedance (Rin).

i.e, XCin = 1/10 (Rin)

Rin = R1 parallel R2 parallel (1 + (hfe re))

re = 25mV/Ie.

Xcin = 1/2∏FCin.

From this Cin can be found.

Finding Cout.

Impedance of the output capacitor (Cout) must be one by tenth

of the circuit’s output resistance (Rout).

i.e, XCout = 1/10 (Rout).

Rout = Rc.

XCout = 1/ 2∏FCout.

From this Cout can be found.

Setting the gain.

Introducing a suitable load resistor RL across the transistor’s

collector and ground will set the gain. This is not shown in  Fig1.

Expression for the voltage gain (Av) of a common emitter

transistor amplifier is as follows.

Av = -(rc/re)

re = 25mV/Ie

and rc = Rc parallel RL

From this RL can be found.