Thank you for  showing your useful information to me.I need the small signal equivalent circuit of pHEMT transistor.  Latter I am connecting my own circuit to pHEMT transistor.From that pHEMT transistor along with our own circuit, I have to draw equivalent circuit for everything. Later I need to obtain equation for NF, linearity, gain, , input impedance, output impedance from the entire circuit. Can you help me , how to get the above parameters from the entire equivalent circuit. 

Thank for your reply and given useful information. Sorry for giving trouble. I am familiar with previous posting parameter such S-parameter, stability, ADS.  If anyone knows, please answer to my question parameters in posting #2. My focus is, how to draw equivalent circuit pHEMT along with our circuit.From that  equivalent circuit, how to obtain related  equation to gain, NF,linearity, input and output impedance.

You need to use equivalent circuit with S-parameters as it is Microwave. Look at your design and bifercate it in three parts. 1) sourcing part or input side 2) Sinking or output or Load side 3) inter connecting channel between input and output

The third catagory is again to be given thought on two subcategories 2a) Series components 2b) shunt components.

The equivalent circuit is to be created in terms of source with its impedance (R & X), Channel impedance (R & X) and Load (R & X)

Now, using S-parametric formula, the equations can be constructed and required parameters can be found out (E G S11 is reflection coefficient etc)

The discussion above is interesting but there are some basics to take care of.

The equivalent circuit is for the the amplifying device, the transistor.In order to solve the amplifier circuit one has first to make DC analysis to determine the DC operating point.

After that the transistor is substituted by its small signal equivalent circuit.

Then the ac performance of the circuit can be determined by the well known circuit analysis methods. One can determine the gain, the input impedance and the output impedance in terms of the circuit elements values. Even one can determine the gain frequency curve of the amplifier.

That is you can derive the performance parameters in terms of the circuit parameters.

You can solve your circuit also by using a circuit analysis software like PSPICE.

Here you need only to graphically enter your circuit in the computer and describe it according the proper syntax. You can even choose your device from the existing library of the transistors. The library has the transistor models both DC and AC .

Large signal models require to get the large signal model as the output voltage

as a function of the input voltage and evaluating the linearity of this relation.

The parameters of the equivalent circuit   can be partly calculated and partly measured. They can be also calculated from the S parameters.

For more information on the HEMT model please see the link:

www.radio.feec.vutbr.cz/kosy/soubory/zahranicni.../mediavilla_01.pdf

For solution methods as an example see the Link:

https://www.researchgate.net/publication/256346392_The_bipolar_transistors_theory_and_basic_applications

Wish you success

Book The bipolar transistors, theory and basic applications

I have drawn the simplified equivalent circuit small signal model for pHEMT transistor along with my bias circuit and input and output coupling.

For this equivalent circuit(Equivalent circuit is attached, Related equation in the equivalent circuit is also attached), can you help me to find out input and output impedance, gain, Noise Figure, and linearity for the attached equivalent circuit small signal model.

As "Abdelhalim Zekry" Sir told

"You can solve your circuit also by using a circuit analysis software like PSPICE"

I have downloaded and installed the "PSPICE" student demo version. How to give our desired circuit to the PSPICE software and how to obtain the desired parameters of our circuit such as input and output impedance, gain, Noise Figure, and linearity.

When I browse the installed "PSPICE" software, it is showing many options such as capture student, pSpice  AD Student, PSpice Design manager    etc..... which option I have to choose and import our schematic and when we give our equivalent, what format schematic should be there. Schematic, I saved in the .jpg and started to import design, it is showing error " it can't be imported, file must be ended with ".ini" format.

Can you help what I have to do. I have shown the screen shots of the PSPICE student installed to my system.

Gagendra, what  is the function of Lf.  Is it added to neutralize the Cdg, the drain to gate capacitance. I did not see Cgd in the equivalent circuit. 

In obtaining the gain, input impedance, output impedance you do not need to consider the noise sources. You merely apply an ac voltage source at the input of the amplifier.

Then you analyse your circuit by using the common circuit theorems in addition to kirchoffs laws for nodes and loops.

Before that you have to be aware of the function of every element in the circuit.

For the Pspice you can attend a training course to be able to use the package efficiently. You have to go the way in a systematic matter. You need training in manual circuit analysis and in using Pspice.

Believe me this is the shortest way to tackle the problem. This is my advise. After that i am ready to discuss an matter with you

Please come back to me.

Abdelhalim Zekry Sir,

        As you asked function Lf . It is feedback inductor, which is used for the input and noise matching. I ignored the Cgd  between gate and drain capacitance in my circuit.

  I have shown in the attachment little modified my equivalent circuit,  for that equivalent circuit, I have obtained the "gain"  equation. Derivation of gain equation is attached in the word file.

I didn't know, how to consider the Lf(feedback inductor between gate and drain) and Ls at voltage across the output. Please I request you, how to include the effect of Lf  and Ls , while finding out the gain.

I request you to check the my Derived equation of gain in the attachment, please guide me how to get the correct gain equation to my little modified equivalent circuit.

When i was in college, a Dr recommended me this book "Fundamentals of Power Electronics" of R. W. Erickson and is the best book that i know that can help you and if you want i can send it to you. 

Can you present the original circuit. Normally such Lf for tuning out Cgd to reduce its effect in limiting the high frequency gain of the amplifier. We have to resolve this point at first. Compensating Cgd by Lf will cancel any coupling between drain and source.

Matching the input source to the input of the amplifier is accomplished by Lg and

Ls. The gain equation you provided is not correct because you assumed that your source is grounded. It i not ac grounded. One way to make the circuit easier  to solve is to substitute  all elements between G and S by an impedance Zgs. and then solve the circuit to get the equivalent impedance between the gate G and ground and then between the drain D and ground.

Dear Zekry Sir,

              You have helped me my all questions previously like anything. I am grateful to you.

             I am facing one difficulty in finding input impedance of my circuit, capacitance is connected between gate and source.

         I  am facing the difficulty ,  can you help to me to get the input impedance  for my circuit  feedback capacitance. If there is any mistake, please point out, please help me to find Input Impedance for attached original circuit.

Dear Gajendra,

You do not need to thank me. You are welcome. 

There is still a basic mistake in your circuit. You have to connect a choke between the drain and power supply rail VDD such that your ac not be shortcircuit via the power supply. Then you have to add at the collector the output load and the matching circuit at the output. The capacitor Cf is of no need. Conversely it may detract the circuit. The feedback inductance has negligible effect on the input impedance if it is made to resonate with Cgd at the center frequency of amplifier operation.

From where did you get this circuit. It has some conceptual mistakes.At first we have to cancel the mistakes and then turn our attention to the effect of Lf on the input impedance.

Best wishes

Dear Gajendra,

I came to again to answer your question. 

The added feed back inductance Lf, will affect the input impedance by shunting the gate terminal to the ground by an admittance called the miller admittance. Accorording to the Miller theorem, this Miller input admittance  y Mi between the gate and ground can be expressed by:

yMi = yf (1- Av), where yf= 1/jwLf , the feed back admittance, Av is the voltage gain of the amplifier. For such inverting amplifier Av will be negative.

Since previously we calculated the input impedance see at the gate say zig as:

zig= gm Ls/ Cgs + 1/jwCgd + jwLs.

This impedenace is connected in parallel with the input Miller admittance, then the overall input admittance seen at the gate including the Miller effect will be

yig total = Ymi + 1/zig= yMi + yig , where yig= 1/zig,

It remains only Lg which is in series with Yig total,

Then The overall input impedance zi will be 

zi= jwLg + 1/ yig total.

This is a complete derivation of the input impedance with feed back inductance Lf.

If any question return to me

Wish you success

Dear Zekry   Sir,

                       Thank you for your elaborate explanation and priceless help to me. Thank you once again.

Dear  Abdelhalim ZeKry Sir,

                       You have helped many of my questions like any thing earlier. I am grateful to you. I need one more help from you.

                       I have drawn the inductive feedback LNA circuit and its equivalent circuit. Can you check once, whether my drawn equivalent circuit for inductive feedback circuit is correct or not.  If it is wrong, where is wrong with that can you tell me. I have placed R1// R2 at the output side is it correct or not tell me. 

                  I request you to check the equivalent drawn circuit for inductive feedback circuit is correct or not, if it is not correct, where I have to correct it, can you advice me.

                Below I have attached the Inductive feedback circuit and its equivalent circuit.

Dear Sir,

      Can you some one clarify it, whether R1//R2 is coming at the input side or output side of the equivalent circuit.

       Can you someone help me.

Dear Gagendra,

Strictly peaking, the inductor L1 is connected to the point Vgg and R1 in parallel with R2 are connected in series with it at the input side of the equivalent circuit. But , practically L1 must be chosen to be high enough to make this path AC open circuit at the operating frequencies. So, the divider resistor together with the L1 can be omitted from the equivalent circuit. Likewise, one can eliminate the path through L2 as i have aid before. So, you need to jut eliminate R1 and R2 from your equivalent circuit and your circuit is okay.

wih you ssuccess

Dear Zekry Sir,

       Thank you for your priceless help. I have query regarding on the Input Impedance of our above said circuit.  Input Impedance simplified it and written below, can you check once, if there is any correction, can you tell me once. Note that I have included the Cgs between gate and source and derived the input impedance circuit, I am sorry for that. If there is any correction, I request you to suggest me.

Dear Sir,

                       Some one can help me to resolve the problem of previous posting.