High frequency model of transistor

 We discussed small signal analysis of BJT  under the key word "Small signal analysis". When input signal to an amplifier is in the range of ten to hundred  Kilo Hertz, a small signal-low frequency model of the transistor can be used for analysis. But as the frequency increases, internal capacitance of the transistor will strongly effect it's performance. A low frequency model cannot work well in this situation. To accommodate these performance changes of the transistor, a separate model  is developed for high frequency operations. This high frequency model is given in Fig 1. A high frequency hybrid-pi model is  also known as Giacoletto model.

Integrator & Differentiator-B Tech university Question & answer

Q1. Explain the working of RC low pass filter, how it can be act as an integrator.

  Answer key: circuit(2), working+fre response(4), act as integrator(5), output(1)                          (12 marks)

 To know, how to prepare answer key, visit link.
 Answer:
Consider a first order RC circuit. It can be act as a low pass filter and allows to pass only the low frequency signals.

Small Signal - Low frequency - Analysis of common collector amplifier-continue

Analysis of amplifier circuit includes derivation of equation for 1)input resistance 2)output resistance 3)voltage gain and 4)current gain. Derivation and analysis of input resistance is given in - 'Analysis of Common Collector amplifier (Emitter Follower) -begins here' . Remaining parameters will be discussed here.

Before beginning, recollect the common collector amplifier circuit and it's small signal model. It was discussed in detail in the -'begins here' post. For your convenience once again giving the circuits.
Here is the amplifier circuit:

fig 1

Small Signal-Low frequency- Analysis of Common Collector amplifier (Emitter Follower) -begins here

We are very familiar with common collector circuits- otherwise known as Emitter follower. Collector terminal is common to both input side and output side. During analysis, we are finding out the nature(characteristics) of the circuit by observing it's input and output resistances, voltage gain and current gain. Here discussing the analysis of CC amplifier using low frequency - small amplitude signals.

Small Signal - Low frequency - Analysis of Common Base amplifier using hybrid model

 Small Signal - Low frequency - Analysis of Common Base amplifier.. Yes, the characteristics of a CB amplifier is analyzing using low frequency -small amplitude signal. Analysis of CE amplifier is in another post. Better to go through it before diving into this.

 As discussed in previous posts, analysis requires three steps - 1)Taking the circuit which is to be analyzed 2)obtaining the small signal model and 3)finding out equations for parameters helps to get approximate values and it in turn will help to predict the characteristics of the circuit.

Small Signal - Low frequency - Analysis of CE amplifier using hybrid π model

 Here we are stepping to a zone mostly liked by questioners for essay - Low frequency analysis of CE amplifier . Small signal analysis of common emitter amplifier can be done using hybrid π model. Here low frequency analysis is considered.

In order to do the analysis of certain circuit, first step is to draw the model of that circuit. This model will help us to easily find equations for certain parameters of the circuit. Usually, input and output resistances, voltage gain and current gain are these four parameters. The equations will give an idea about the approximate value of these parameters and this in turn will help us to comment about characteristics of the circuit.  

Let's start...

Small signal model of a circuit

'Small signal analysis of CE, CB, CC configurations using hybrid π model' is a major topic in 'Micro electronics syllabus'. To do the analysis of a circuit, first we have to draw a model for that particular circuit(CE,CB or CC).  How can we obtain a small signal model for a circuit?- It is explained below. 

Steps to obtain a model from corresponding circuit :

Transistor - small signal model and small signal parameters

Analog Circuits /Electronics Circuits syllabus is packed with models. 

( I can see twinkling in your eyes, but… plz don’t disappoint. Just scan through below lines.)

The model 

To study the behavior of a transistor for different input conditions, we make use of different transistor models. These models are designed by taking various parameters of transistor into consideration. Hence having the same behavior as that of the corresponding transistor. To test the behavior of a transistor for a new input condition, instead of conducting a practical experiment, these inputs are applied on the corresponding transistor model and outputs are measured. Thus 'the model' helps to predict the nature of a transistor(or circuit) for various input or bias conditions without actually wiring it.

Transistor analysis - Small signal analysis and Large signal analysis

We can divide analysis of diode and transistor into Small signal analysis and Large signal analysis.

Large signal analysis

While doing a large signal analysis, a large dc voltage is applied and find out the behavior of diode or transistor towards this signal(find an operating point of these components). The voltage applied are of the order of few volts to few tens of volts. Here we use current and voltage equations such as 

to find bias points. This analysis is applicable to any value of current and voltage applied to the devices.

Small signal analysis

Small signal analysis approximate nonlinear behavior of  electronic components with linear equations. This approximation is taken across the bias point.

Stability in Collector-to-Base bias

This is one of the circuit which is used to provide biasing for BJT. Voltage divider bias and fixed bias are other biasing circuits. In collector-to-base circuit, resistor R_B connects collector terminal of BJT to base terminal, the specialty of the circuit .. This resistor provides a negative feedback and it helps to reduce variations in the operating point. 

Circuit diagram:

fig 1

Fixed bias circuit - Stability factor

Fixed bias circuit is the simplest biasing circuit for BJT. If an equation can be obtained for it's stability factor, we can easily comment about it's stability. Let's begin..

Circuit diagram for fixed bias           

fig 1

The simplest biasing circuit but has least stability.

Voltage divider circuit - stability factor (Sβ)

Myself  Stability factor S_β. My address is . 
To view my history visit  Stability factors & Biasing circuits

 

Request you to visit my Seniors also-    Voltage divider bias - Stability factor 'S' 

                                                                                                                                                          and             

                                                                         Voltage divider circuit - stability factor (Sv)

Referring to Thevenin's equivalent of Voltage divider circuit(fig 1)- ( details are given in Voltage divider bias - Stability factor 'S'   )- equation for Thevenins voltage is given below.

fig 1

Voltage divider circuit - stability factor (Sv)

We are going to catch "Sv"  for voltage divider circuit. "Sv" indicates a stability factor used to discuss stabilization of the circuit during variations in Ic with respect to VBE .  Before starting, it's better to take a trip through Stability factor 'S' for voltage divider circuit . Also for getting more idea about stabilization and stability factors, plz visit Stability factors & Biasing circuits .

Stability factor (Sv)

Stability factor indicates the stability of the circuit which is under discussion. Stability means variations in operating point(mainly Ic). To find 'Which are the main components in the circuit that affects stability?' -we always depends upon the equation for the stability factor. Once we get it, we can easily find the components affecting stability and it will then lead us to 'different ways for increasing stability'.
Consider the Thevenin equivalent  for Voltage divider circuit. A detailed description is given in the post Voltage divider bias - Stability factor 'S'. For convenience i am including Thevenin's equivalent of input side of voltage divider circuit(fig 1).

fig 1

 On writing loop equation, we will get as,

Voltage divider bias - Stability factor 'S'(Stabilization in voltage divider circuit)

Various biasing circuits are designed for amplifiers(a refreshment is provided here). One which is familiar to you is Voltage divider bias, also known as Self bias. Here, we are discussing about various stability factors in self bias.

First, consider diagram for voltage divider bias :

fig 1

This is the commonly used biasing circuit as it provides good bias stability. It is connected in Common Emitter configuration. In order to connect as an amplifier, Emitter-base junction is to be

Stability factors & Biasing circuits

Stability factors seems to be  heavy???. Make a trip along with fundamentals of BJT- plz click here - BJT - first glimpse

Stability factors & Biasing circuits: 

An idea about biasing and stabilization will help in the study of Stability factors -plz check the following paragraph.

Things to be ensured before wiring an amplifier:

Before setting up an amplifier circuit, operating point should be fixed at an appropriate position on the load line - preferably at the center of the load line. This can be done with the help of a biasing circuit. It is also to be ensured that the operating point does not shift due to changes in temperature or due to variations in transistor parameters(see explanation below) - in other words operating point should be stable.

The maintenance of the operating point stable is known as stabilization.

BJT - first glimpse (Biasing in RC coupled amplifier and Q point)

A vital part of an electronic circuit is a transistor . One which is familiar to you is Bipolar Junction Transistor(BJT). Just take a tour through the necessary points. Here include the basic equations related to transistor. Also explain the concept of biasing and Q-point with the help of an amplifier circuit.

fig 1

Clamper

 The word Clamp means 'to hold things together or fasten two things together'. In electronics it means 'hold voltage level of a wave at a particular value which is different from its normal.

Clamping circuit is used to shifts a signal by a dc voltage. How it is possible to shift a sine wave?

Fig a

This dc level shifting is explained in Fig a. Dc level of  sine wave (leftmost figure) is at zero volt. Sine waves having dc level at +2v and dc level at -2v are followed. A clamping circuit can be used for this purpose. 

Clamper circuits -section I

A simple clamping circuit is given below in fig 1. The circuit consists of a capacitor and a diode. Across the diode output voltage is taking. Here the capacitor act as a battery(Capacitor has a charge storing capability and thus can be act as a cell. At the first instant of switching on the circuit, capacitor is charged to maximum value of input voltage(Vm). It will maintain this voltage in it until the input is switched off). In fig 1, positive side of the diode is at the top side and so leftmost plate  of the capacitor is positive(current direction through the diode is from top to bottom and that in capacitor is from left to right - so left plate is taken as positive. Since right plate is negative, donation to output voltage by the capacitor is negative).

fig 1

To get an idea about how the output is obtained, keep these two things in mind:
1.During positive half cycle of input voltage, diode is forward biased and no input voltage is dropped across diode(so no donation to output voltage by diode). But our capacitor battery is there, and its voltage(Vc) is equal to maximum value of input sine wave(Vm). Then have a look into voltages in the circuit.

 Positive half cycle of the input sine wave is shown with Vm=10v, its polarity is also indicated. Capacitor is charged to 10v with polarity as shown. Since diode is forward biased it is represented with a small forward resistance. Output voltage is taking across points 'a' and 'd'(Vad). Vad = Voltage across 'abcd' =  -Vm+Vin = -10v+ Vin. (Vin is varying from 0 to +10 then to 0). So -10v +Vin will be as follows:

                                                This is how the output in fig 1 is obtained during positive half of input.

2. During negative half cycle of input, diode is in reverse bias and it will behave as an open circuit.

Now have a look into polarities of input voltage and capacitor. Since capacitor charges only during the positive half cycle of input sine wave, polarity is same. But because of negative half cycle of input, polarity of Vin is reversed. Output voltage is taken across points 'a ' and 'd' (Vad). Vad = Voltage acrosss 'abcd' =  -Vm -Vin  =  -10v -Vin. 

This explanation is only for keeping in your mind, don't pour it into your papers. Only one thing you need to do is --- assign a polarity for the capacitor according to forward bias condition of diode. If  -ve polarity is nearer to diode, keep in mind that output will be in the -ve side of Y axis. Keeping circuit of fig 1 in mind, it is easy to find outputs of fig 2 and fig3. Lets see..

fig 2

 Compare outputs of fig 1 and fig 2. If output of fig 1 is slightly shift towards top we will get output of fig 2. This shift is because of the presence of positive cell voltage Vr.

fig 3

Similarly if we shift the output of fig 1 towards bottom, output of fig 3 will be obtained. This is due to negative battery voltage Vr attached to the diode.

Clamper circuits - Section II

It is easy to diegest  the remaining circuits if we relate them to that in section I. Just reverse the direction of diode in fig 1, then look below. Yaa, next circuit.

fig 4

 With the reversal of diode, don't forget to reverse the polarity of capacitor - here current direction through the capacitor is taken from right plate to left plate. A tip to remember - if the capacitor plate nearer to the diode is positive then output wave will be in the positive side of y axis.

Follow the same route of transition from fig 1 to fig 2, for fig 4 to fig 5..

fig 5

 When a  positive bias is introduced into fig 4, we get fig 5 and waveform shifts up.

Then again find an old route, that is from fig 1 to fig 3 and follow it for fig 4 to fig 6.

fig 6

With an extra negative bias in fig 6 compared to fig 4, waveform shifts down.



Easy???

Combinational Clipper Circuit

This is a continuation of 'Clipping Circuits'. In a simple clipper circuit either +ve or -ve half cycle of sine wave can be altered at a time. Using a combination clipper circuit, both half cycles can be shaped using a single circuit.

fig a

 Circuit in fig a is a combination of fig 2 and fig 5 in 'Clipping circuits'. Its easy to understand the output waveform by considering +ve half cycle of fig 2 output and -ve half cycle of fig 5 output.

fig b

Circuit in fig b is a combination of fig 2 and fig 6. Here also the output can be easily find out by combining output of fig 2 and fig 6. (In fig 6, bottom side of +ve half cycle of sine wave is removed. In fig 2, topside of +ve half cycle of sine wave is removed. Apply some logic and combine two - in a +ve half cycle of sine wave top and bottom side are removed - that is given in above fig b.Please forget about the -ve side of sine wave - there is no alternation for -ve side in fig 2 and nothing is there in the -ve side of fig 6.)

fig c

Circuit in fig c is obtained from fig 3 and fig 5. By removing both sides of -ve half cycle of sine wave, output of fig c is obtained.

Clipping Circuits

Clipping circuits are used as wave shaping circuits. Usually it is used to shape sine waves by cutting off some of its parts, but it can be used for other waves also.The idea will be clear if we familiar with the simplest member of clipper family. 

An example of a clipper circuit is Half wave rectifier. Circuit, Output voltage ('Vo' vs 't' -obtain using CRO) and Transfer characteristics  (' Vo' vs 'Vin' -obtain using CRO) are shown.

fig 1

Here i take two circuits -one in top and other in the bottom position, both give same output, hence same transfer chara. Though you know very well about the working, am just briefing it - for my convenience. Circuit in the top consists of a resistor(R) and a diode(D). Output takes across D ie. CRO probes are connect across two ends of D. 

For positive half of input sine wave, D is in forward bias - current is flowing without any resistance, so voltage zero(diode ON). //A voltage is developed only across a resistance, if resistance of a component is zero then voltage across it is also zero. But this an ideal situation only - not practical. Every component, even 'diode in forward bias' have a small resistance (ON resistance), therefore a small voltage across it ie. 0.7v //

For negative half cycle of sine wave, D is in reverse bias. No current flow through D. Diode act as 'Open circuit'. So whatever the voltage applied in the input side, is completely appeared across D - in other words, output follows sine wave's(input) negative half cycle. //When there is no current flow through a component, resistance of it is taken as infinity(resistance=voltage/current). Comparing to this infinite resistance, all other resistances in the concerned circuit are negligible(even though it has any value -K ohm/M ohm/..). We know V=RI, since resistance is infinite, voltage is very high(not infinite). Therefore whatever the voltage given as input to the circuit, that full voltage is dropped across this infinite resistance. ie. voltage across an 'open circuit' = input voltage --all other components in the concerned circuit have negligible voltage.// 

   We can easily draw transfer chara using input and output waves. Below given explanation will help you for it.

Transfer characteristics : It means input vs output.When both input and output are sine waves, transfer chara is 

fig a

When Vin increases +vely (in transfer chara, from (0,0) towards right), Vout also increases +vely(in transfer chara, from(0,0) towards top). Result is a straight line with 45 degree slope. Similarly for -ve half cycle also.   

Now let's see how transfer characteristics is obtained in fig 1. Take fig a, as reference. Consider transfer chara of fig 1. For +ve half of Vin, Vout is constant at 0.7v - so transfer characteristics is a straight line at 0.7v(output is constant at 0.7v irrespective of change in input). It is indicated both in output waveform and transfer chara. For -ve half of Vin, fig 1 is same as fig a.

Hope the above explanation is satisfactory. Now move to next clipper circuit.

fig 2

 Explanation for obtaining such an output is as follows: We are adding a +ve bias (+ve voltage) in the basic circuit(fig1) using a battery and it shifts the cut off voltage of diode from 0.7v to (Vr + 0.7v). Vr is the voltage of battery(we can use 5v or 7v or any other, but should be less than Vin). You can easily understand its transfer chara by comparing it with fig a.

Next clipper is obtained by adding a -ve bias to circuit in fig 1. It shifts the cut off voltage to (-Vr + 0.7v).

fig 3

 It is easy to remember the output of fig 2 and fig 3 by relating it to output of fig 1.

(i)adding Vr to output of fig1     (iii)output of fig2

(i)adding -Vr to output of fig1     (iii)output of fig3

No need to study theoretical explanation of how to obtain the output for a particular clipper circuit. Such essay questions are not yet asked for theory exams. But short answer questions may be asked and it will be like 'given a transfer chara. draw the corresponding circuit'. To answer such questions, first you draw the output wave form using given transfer chara and then the circuit.

Next look into next set of clipper circuits. Here circuit in fig 4 is taken as the basic circuit and is obtained by reversing the diode in fig 1.

fig 4

In fig 4 cut off is at (-0.7v) and is an example of a half wave rectifier. Now see what happens if a negative bias is added to circuit in fig4.

fig 5

A - ve bias of (-Vr) is added to fig 4 to obtain circuit in fig 5. Then cut off voltage changes from -0.7 to (-0.7-Vr). It is adopted in output waveform and transfer characteristics. Similarly if a +ve bias of Vr is added to circuit in fig4, we will get circuit in fig 6. Cut off voltage is shifted to (-0.7+Vr). //For example, battery voltage Vr =5v. Then cut off voltage is -0.7+5 = +4.3//

fig 6

These are the simple clipping circuits. Once you familiarized them, move to combination clippers

RC Differentiator

High-pass RC circuit as Differentiator:

Adding some ‘salt and pepper’ over high pass RC circuit will give differentiator.
In differentiator output voltage, Vout is proportional to the rate of change of input.

     

Circuit diagram:

As in the case of integrator, when the high pass circuit obey some condition, it act as a differentiator. Shall we see how it is?

Lets write the equation for output voltage.



//output is taken across R and R+1/CS is the total resistance of the circuit. So applying voltage divider rule, Vout = Vin{ R/(Total resistance) } //

Laplace transform s=jw (w=2πf) and RC is the time constant.



Rearranging,
     
 
Take the condition that RCw << 1, then

 

// When RCw << 1, then 1/RCjw become large, so 1+1/RCjw is approximately equal to 1/RCjw. Now the equation become
//

We know jw = S, Laplace transform. So

therefore, Vout = RC S Vin

The above equation is a Laplace equation and we take inverse Laplace, then equation become,



Equation shows that output voltage is proportional to derivative of input voltage. So the circuit represents a differentiator circuit.
OK!! then go through output of the differentiator circuit for different inputs.

                                                                                                           



                                                 
                        
















//In lab hours, select different R and C and check output.Also check output just by changing input frequency(by adjusting front nob of  signal generator) //

 If we make a chicken fry, what is next?. Check its taste, whether salt, chilly etc are ok. Likewise if an output is obtained some people check its different properties and we people study it. So two properties of output wave form.

Rise time (tr): The time taken for the output voltage to rise from 10%  to 90% of final value.
//if peak is 100 v, then how much time the wave will take to rise from 10 v to 90v.//

Delay time (td): The time taken for the output voltage to rise from 0 to 10% of its final value.

Low pass RC - integrator and high pass RC - differentiator are very important in lab exams. It will ask in combination with Rectifiers. For theory exams it is not a usual question. Something bigger is going to happen... 

Come back with some interesting circuits..