First of all, I’m sure you ment Vds >= Vgs – Vth for a MOSFET in saturation. Vds is defined as the potential difference between drain and source, Vgs as the potential difference between gate and source. simulate this circuit – Schematic created using CircuitLab By shorting gate and drain, they…tlfong014705Your answer is excellent, and newbie friendly to me with IQ 97. I really appreciate your suggestion at the end of “taking deep look, … wrap my mind around the fact that *three quantities are plotted in the same graph, …”. I studied a EE diploma ages ago, and I confess that when reading about linear/saturation region of BJT operation, I had not taken a deep enough look at the graph, and so I did not know, as you said, three quantities are plotted on the same graphs. / to continue, …At that time I only knew a basic graph with X- and Y- axis. I never thought that there can be a graph with three axis, X, Y, and Z!to make sure I thoroughly understand your answer, I use the following MOSFET as a case study: IRL540N 100V N-Channel Power MOSFET Datasheet – Infineon: infineon.com/dgdl/…. I read the data sheet and I have two questions related to the linear/saturation region. The questions are written in the following picture: i.imgur.com/zNX2E4W.jpeg. I am designing switching circuits using this IRL540N. I would appreciate it you can answer my questions. Thanks a lot. Cheers.Thank you very much for your quick and very helpful answer. Your guess that shorting gate and drain as a useful convention is very reasonable, and I would have never thought about that. And because I have not seen such a condition in BJT datasheets, I need to google more MOSFET data sheets to convenience/verify myself. BTW, I am a slow thinker, so it might take me sometime before I let you know my research/verification results. Have a great weekend. Cheers. StrugglingStudent117I would like to clarify that my book defines threshold voltages as Vtn and Vtp. Not Vth. Theydo it to not confuse with thevenin voltage so that’s how i write it now. Excellent answer. tlfong014705@StrugglingStudent117, I appreciated your clarification very much. Earlier I said I need to use URL540N as case study to “translate” #K. Krull terms to what I know, because I I found his use of terms confusing. I have never read any books on MOS, and I only focus on two parameters: (1) Rds(on), (2) Vgs(th). I don’t even care of Vds, because I only play with Logic level trigger N-Ch power MOSFETs. Your question mentions terms like λ, W, L which I never heard of. So I knew I have no prerequisite knowledge to understand your question. / to continue, …However, I was curious to know what you are talking about, so I googled something to read. I guess some other newbies and future readers might also are interested, so I am listing some of the things I might read. The first one is (1) MOS Field-Effect Transistors (MOSFETs) Sedra8e Solved Problems Ch05 (1) (λ W/L etc): learninglink.oup.com/protected/files/content/file/….And I second reference I might read is the following: (2) Jaeger & Blalock, 4th Ed, Ch 4 Problems … – UW ECE (The OP’s question is 4.34) dunham.ece.uw.edu/ee331/JB4edProb/…. Ah lunch time. See you later.The third reading is this: (3) (PDF) Microelectronic Circuit Design by Jaeger 4th edition.pdf – Academia.Edu academia.edu/35781367/…@StrugglingStudent117, The title of Jaeger’s Microelectronic Circuit Design, misled me to think that it was a boring book on MOSFET fabrication, which is what I am least interested, because me EE hobbyist focuses only on application, not at all fabrication. But then when I skimmed the book’s preface, I guess the book should be interesting. So I skimmed on the first three chapters, spending about 30 minutes. I found it a good comprehensive introduction book (I give 5 stars or 9/10) for EE newbies, … My long winded comments stops here. I will begin reading Ch 4. See you later. StrugglingStudent117167@K.Krull Why does the red line look exponential? Like an e^x function?Like it would seem that the red line is it’s own graph WITHIN a graph.. Vds as a function of Vgs – Vth. Sort of ignoring the current on the y axis and instead using Vgs as the Y?. This looks like two graphs with two different Y axis on ONE. tlfong014705@StrugglingStudent117 Do you think k.Krull’s “red line” is the “Pinch off locus” – Fig 4.8 (4.2.4 SATURATION OF THE i -v CHARACTERISTICS) ?@StrugglingStudent117 Ha, your looking at the i-v graph as a “graph within a graph” is what I see as a “three dimensional graph”. Krull is interpreting the graph as something showing a relation of three quantities. You can also see it as a relationship graph showing how one dependent variable Id, is relates as two independent varies Vds and Vgs(th).Actually you can extend 3 variables to 4 variables: Id depends on Vds, Vgs(th), and T (temperature). Our stupid 2 human eyes can only “see” 3 variables as 3D. If there are 4 variable or more we can no longer “see”, but we can “see” them mathematically, as “tensors”, all crazy scientists Einstein like mathematical equations, no more graphs! 🙂I appreciate your description of “This looks like two graphs with two different Y axis on ONE”. Now let me ask you a follow up question: So for 4 variables, Id, Vds, Vgs(th) and T (temperature), will your have 3 graphs of 2 different (overlapping) Y axis?Any way, let me tell you my Jaeger book reading report. (1) I skimmed Sections 4.1 and 4.2. I found them very good, giving we newbies a solid background based on equations (No, I did not “proof read” Pro Jaeger’s mathematics, I trust him, as I trust Einstein of his equation “E = MC²”). I also now know what he means by W, L, λ etc.Coming back to the confusing thing of shorting out Source and Gate, I tend to see it is just an academic exercise, just to train the students’ minds. I mean shorting S and G has no practical applications, but just scare the students to study hard! (only 50% sure) 🙂I am glad that you have asked an interesting question and guided me to find the very good book by Jaeger book. I am now giving his book 9.5/10. Ah, jogging and locking up supper time. See you later. 4 hours later… K. Krullyst 21:41@StrugglingStudent117 The red line is not an exponential, but quadratic. This is due to the quadratic nature of Id vs. Vgs-Vth (note the increasing distances between the blue curves, allthough Vgs-Vth has linear steps). This quadratic behavior is then plotted against a linear axis for Vds, which gives us a quadratic parabola. 17 hours later… tlfong01470514:37@K.Krull Ah, I learnt quadratic equations in middle school algebra but I forgot what it exactly is. So I ask Wikipedia that says the following: “In mathematics, the term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree, or equations or formulas that involve such terms. Quadratus is Latin for square.“I do not remember earlier when I skimmed Cha 4, section 1,2, I did not see any equation with square terms. Perhaps I must skimmed again. Anyway I think the curve is NOT exponential, because MOS is not related to diodes or P-N junctions, which is modelled using exponential functions of Euler number e and Boltzman constant ktlfong01470515:07As Jaeger says, the “pinch-off locus”, which separates the linear and saturated region, is the series of points at different Vgs, each points of which is the intersection of two equations (an example at Vgs = 3V), as illustrated below:
At the end of the NMOS lecture, Pro Jaeger gives a summary of the mathematical model of NMOS with a couple of equations which the miserable struggling students (Thank God not me!) must memorize by heart. The equations are integral, so should not be considered as quadratic, I think.