Finding op amp Gain and Beta using LTspice - Page 1
Forum section: electronics / beginners

author: Shay
author_rank: Regular Contributor
timestamp: January 27, 2025, 06:32:24 pm
content: Hello,I am tasked with finding the gain and beta at a specific Frequency.Finding the gain is not hard, but I am unsure how to find the beta in those questions as they are not trivial and have some positive feedback. How is it done? It is fine to use LTspice.Please see the attachment.Thanks

author: wasedadoc
author_rank: Super Contributor
timestamp: January 27, 2025, 06:51:36 pm
content: 1. que3 has one side of the input connected to the output. That does not seem correct.2. What is beta?

author: Shay
author_rank: Regular Contributor
timestamp: January 27, 2025, 09:44:05 pm
content: Quote from: wasedadoc on January 27, 2025, 06:51:36 pm1. Yes, probably because it is not correct, which I noticed now as you pointed it looks wrong.The writer of those questions makes a lot of mistakes.2. Beta as in β.

author: tszaboo
author_rank: Super Contributor
timestamp: January 27, 2025, 10:28:02 pm
content: This looks like homework to me, because:- no sane person would connect the input this way- nobody cares about beta after graduation

author: mikerj
author_rank: Super Contributor
timestamp: January 27, 2025, 10:40:56 pm
content: Quote from: Shay on January 27, 2025, 09:44:05 pmIt's not wrong, the circuit is designed to make you think a bit. Referencing the input signal on the inverting input to the output signal gives 100% negative feedback, i.e. a gain of one. Adding feedback to the non-inverting input will increase this. Use the regular non-inverting op-amp gain equation (1+30k/20k) and you'll find this circuit gives a gain of 2.5

author: Shay
author_rank: Regular Contributor
timestamp: January 27, 2025, 11:08:23 pm
content: Quote from: tszaboo on January 27, 2025, 10:28:02 pmThis is homework, but not my homework. I am just trying to help and understand myself since I rarely encounter those types of questions in the practical real world as a hobbyist.Quote from: mikerj on January 27, 2025, 10:40:56 pmYes, but the question is how I derive beta from this. If it is just to look at the non-inverting part then the beta is 0.08 at 100kHz. Is that correct? I derived it by understanding that beta is the portion of the output voltage that is fed back to the differential opamp input (input source grounded). thus we get:att1.png(3.47 kB. 279x153 - viewed 297 times.)where Vfb is 80mV for 1V input, so the beta is simple 0.08.

author: Terry Bites
author_rank: Super Contributor
timestamp: January 28, 2025, 09:15:43 pm
content: Beta is not an opamp parameter. Beta is the "feedback fraction" created by the feedback network (divider).You answer the question by learning your network theory. If you simulate it you learn nothing.

author: Shay
author_rank: Regular Contributor
timestamp: January 30, 2025, 01:20:09 pm
content: Quote from: Terry Bites on January 28, 2025, 09:15:43 pmThe question is given to a mechanical engineering student who does not have the time nor the need to understand network theory. I agree with you in general, but in this circumstance, I am just looking to find the answer with simulation. (I am not the mechanical engineer but rather just trying to help). There is a time and place for everything.

author: Zero999
author_rank: Super Contributor
timestamp: January 30, 2025, 02:59:18 pm
content: Please post the .asc file in future.I've simulated it myself.It's an unconventional circuit, which appears to have been designed to confuse you, but it's not that complicated.Remember an op-amp always maintains the feedback loop to keep both its inputs at the same voltage.

author: MrAl
author_rank: Super Contributor
timestamp: January 31, 2025, 11:42:19 am
content: Quote from: Shay on January 27, 2025, 06:32:24 pmHello,First, in theoretical academic problems like this an input voltage connected like that would not be without precedent. That means it could actually be like that. There's always the chance that the schematic is wrong in any problem though so if you suspect that then you have to refer to the author.Beta here would refer to the factor Vn/Vout where Vn is the voltage at the inverting input terminal. If you already know the gain then this should not be too hard to calculate. The only difference is that since we are going to use Vout and Vn rather than the external components themselves, the positive feedback is already accounted for in the calculation for Vout. The components themselves will appear in these two calculations.It may seem unusual because you are probably used to seeing circuits with only negative feedback, and then the Beta could be calculated by the external components, but since there is positive feedback as well as negative feedback that becomes a little harder to do although not impossible. Since we can also look at the two voltages though it becomes easier to calculate as long as we can calculate the output voltage. To calculate the output voltage we first choose an op amp model, then proceed with the circuit analysis as usual until we arrive at the output voltage. If the circuit is valid, we then have the output voltage. We also calculate the voltage at the inverting input terminal, then we can calculate the theoretical Beta.There is one caveat, and that is that when we have some positive feedback we have to check for a latch up condition. That would mean the circuit is not entirely linear.There is another catch and this one is kind of hard to deal with. That is, if the professor that handed this problem out is prone to error, then it is also entirely possible that he arrived at the wrong result. That means even if you get the right result it will still look wrong to him. The only way to resolve this is to talk to him and go over the calculations together. Unfortunately, I hear a lot of students telling me that the instructor is not responsive, which can make life difficult.If you do get a result that differs from the given result, you can try changing the topology a little and see if you can get the right result that way. if you do, then it may mean that he actually did draw the circuit incorrectly.

author: MathWizard
author_rank: Super Contributor
timestamp: February 03, 2025, 10:41:05 pm
content: Quote from: tszaboo on January 27, 2025, 10:28:02 pmSo why do you say that ? Would people just use a simulator and not calculate something when designing stuff ?

author: mtwieg
author_rank: Frequent Contributor
timestamp: February 04, 2025, 01:36:42 pm
content: Quote from: MathWizard on February 03, 2025, 10:41:05 pmThere are other methods to analyze circuits. IMO the "beta" approach to solving feedback circuits is pretty useless, it's always easier to solve by just applying KVL + KCL directly.Though it's not nearly as bad as the series/shunt topology approach, which IIRC was a miserable trash fire.

author: MrAl
author_rank: Super Contributor
timestamp: February 04, 2025, 11:56:11 pm
content: Hello again,This can be very simple if we take a look at a block diagram of a system (see attachment).In Fig 1, we see a general feedback system with both negative gain (H) and positive gain (K) feedback.In Fig 2, we see a feedback system with the feedback gain only equal to Beta.To get from Fig 1 to Fig 2, all we had to do was subtract K from H and make that the Beta:Beta=H-KThat's about as simple as it gets.One little note though. That is, we have not considered any input or output impedance effects which is often part of the system. In this thread we did not need to consider that though because we assumed the output impedance of the op amp was zero.

author: CatalinaWOW
author_rank: Super Contributor
timestamp: February 05, 2025, 01:51:29 am
content: Just a comment on how important context is. I had never seen the beta terminology in association with feedback loops. This is not a product of limited control experience, I had multiple feedback and control courses through graduate level, and utilized various op-amp filters and feedback systems through my career. I can see the benefit of this characterization, but in the particular educational and operational environment that I live in just never encountered it. My only electronics usage of the term came as reference to the current gain of a transistor. Had no idea how to answer this question with that definition.

author: Jay_Diddy_B
author_rank: Super Contributor
timestamp: February 05, 2025, 02:11:03 am
content: Hi group,The equation in Fig 2:Vout = Vin * Aol / 1+ Aol * BIs very important inprecisioncircuits.In an ideal op-amp Aol = infiniteAol /1 + Aol = 1But in a practical op-amp the value of Aol is typically 120 to 130dB Meaning Aol = 1E6 to 5E6So Aol/1+ Aol = 0.999999 introduces 1ppm of error.For most other circuits:Vout = Vin * Aol / 1+ Aol * B = Vin/Bbecause Aol/ 1+Aol can be treated as 1.Jay_Diddy_B

author: Zero999
author_rank: Super Contributor
timestamp: February 05, 2025, 09:24:49 am
content: The open loop gain needs to be > 10*beta, to get within 10% of the desired gain, 100*beta to get within 1%, 1000*beta to get within 0.1% etc.EDIT:Schematic & plot added.X axis: open loop gain, swept from 100 to 1M.Y axis: output voltage.

author: tszaboo
author_rank: Super Contributor
timestamp: February 05, 2025, 09:32:20 am
content: Quote from: MathWizard on February 03, 2025, 10:41:05 pmBeta usage is control theory applied to an electronic circuit. It's bad practice.Same way as you don't start to solve Maxwell's equations when you want to calculate antenna's range.Or you don't try to simulate linear circuits in Matlab. You do that with some Spice simulator. It's not the right tool for the job.

author: MrAl
author_rank: Super Contributor
timestamp: February 05, 2025, 04:23:07 pm
content: Quote from: CatalinaWOW on February 05, 2025, 01:51:29 amI had to give a lot of "thanks" in this thread, but to me that means "like". I liked a lot of the replies in this threadHi,Yeah, this kind of theory is sort of in a world of it's own. That means some things get overlooked too.I had one experienced engineer ask me why my calculations of a particular system did not come out the same as his, when he used this "Beta" theory idea. It turned out that the input and output impedance made all the difference, which the theory he used did not account for. It's sort of simplistic in its nature, an attempt to make things easier in some situations. I don't consider it a full blown analysis.This is the way it is with a lot of 'theories' though in electronics. Sometimes there is a simple method that really only works in some situations, but it's taught anyway. To me it would be a sort of beginners method. It's sort of like the difference between using just Beta for a transistor versus using the Shockley equation. The Beta version Ic=Beta*Ib works in a lot of situations and makes it easier to understand the amplification of a transistor, but we have to know its limitations such as when the transistor is in saturation.This probably happens a lot because these ideas are handed down one person to the next without a full explanation of what the limitations are, and many people do not want to take the time to learn a complete circuit analysis technique, or even network analysis.