# Why does voltage gain of fixed bias transistors not as same I calculated ?

#### MrChips

Joined Oct 2, 2009
28,095

1) by calculation
2) by simulation
3) by real circuit measurements

Which one gives the "correct" answer?

#### WBahn

Joined Mar 31, 2012
28,138

1) by calculation
2) by simulation
3) by real circuit measurements

Which one gives the "correct" answer?
#1 almost never does, but we have developed techniques so that these should be in the ballpark and, in many circuits, useable with little or no modification.

#2 should be the one to go with since the simulations can take into account far more variations then prototypes can. But you have to have good enough models (which usually do exist) for this to be the case.

#3 produces results which are, pretty much by definition, correct for that particular set of components operating under those particular conditions. This, of course, is even assuming that prototyping the circuit is even an option.

#### Heroz

Joined May 29, 2022
31
#1 almost never does, but we have developed techniques so that these should be in the ballpark and, in many circuits, useable with little or no modification.

#2 should be the one to go with since the simulations can take into account far more variations then prototypes can. But you have to have good enough models (which usually do exist) for this to be the case.

#3 produces results which are, pretty much by definition, correct for that particular set of components operating under those particular conditions. This, of course, is even assuming that prototyping the circuit is even an option.
Sorry I have a question . Can you give an example about calculation techniques ? So it means that Multisim is wrong medel right?

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#### MrChips

Joined Oct 2, 2009
28,095
Even something as low as a 10Ω resistor in the emitter leg makes a big difference on the gain.
It reduces the gain by a factor of 2.

#### Heroz

Joined May 29, 2022
31
hi Hero,
There is a spread in the parameters for most semiconductor devices, this is mainly due to manufacturing.
I use the typical values from the device's datasheet, other users choose the lowest parameter listings.
E
@ericgibbs Does LTspice model use typical values ?

#### WBahn

Joined Mar 31, 2012
28,138
Sorry I have a question . Can you give an example about calculation techniques ? So it means that Multisim is wrong medel right?
A transistor is a highly non-linear device and so analyzing and designing circuits that use them would be, in general, difficult to do even if we knew exactly how every transistor behaved. So we develop analysis techniques that rely on approximations that get us close to how the actual circuit works -- treating the voltage drop across a forward-biased diode (or the base-emitter junction of a bipolor junction transistor) as a constant voltage regardless of current is just one example. We take this a step further and develop techniques, such as small-signal analysis, that let us treat the transistor as if it behaves like a linear element provided certain conditions are met. We then design circuits that try to ensure that those conditions are met.

Unfortunately, on top of the nonlinearities (which, by the way, are not always a bad thing -- lot's of circuits, such as radios, rely on that nonlinear behavior in order to function), is the fact that many of the properties of transistors (and nearly every other electronic component, but transistors are among the worst) vary greatly. Not only do the properties of the same transistor vary depending on lots of variables, including voltage and current and temperature, but also two transistors operated under identical conditions will vary, even if they were manufactured on the same silicon wafer. So once again we develop design techniques that use circuits intended to reduce the sensitivity to these variations and methods to ensure that the circuits behave within acceptable limits regardless of what the parameters of a particular component happen to be at any given moment. We can do this to some degree manually by using very conservative designs that are checked at the extreme limits of a component's possible values for key parameters, but our ability to do this is very limited in all but the smallest circuits and we can only consider a few parameters -- the number of possible combinations are just too vast.

Simulators, on the other hand, can perform statistical simulations in which they randomly vary as many parameters as we want over their range of possible values and then run a simulation and capture the result and then repeat the process hundreds of times, or even millions of times, and then we can view what the expected range of performance outcomes are and decide if it is acceptable.

But any simulation is only as good as the models for the devices it uses. For a transistor that's been around for as long as the 2n2222 and has been made by as many difference manufacturers on as many different fabrication process lines as it has, it is not surprising that there are a lot of different models out there that have been developed over the years. It's difficult to say which of them are "good" or "bad" because it's pretty much guaranteed that any one of them is really only representative of a fraction of those versions that have been made.

This, again, is where design strategies that mitigate the effect of these differences come into play. Your circuit relies on being able to accurately estimate the small-signal emitter resistance and output resistance of the transistor. A good design would be such that these could vary over a significant amount without having a huge impact on the circuit's behavior. We generally do this by using external components and negative feedback mechanisms in order to sacrifice some of the high gain we could get in favor of getting a smaller, but much more reliable, gain.

#### Heroz

Joined May 29, 2022
31
Now I'm confused between BF and beta, Hfe . Is it the same thing? In LTspice BF is 200 but Multisim is 153 first I think that BF is beta , Hfe and beta = Ic/Ib . Both of Multisim and LTspice , Ic and Ib are close therefore beta also are close but BF is different.
Does that mean beta and BF are different?

#### WBahn

Joined Mar 31, 2012
28,138
In my main question I used my calculation and voltage gain is 713 but in LTspice it's 535 . My calculation is correct right ? But there is some percentage error in my calculation because In LTspice they use many parameter to calculate right?
The big difference is that your model of the small-signal response did not take into account the finite output resistance of the transistor.

In the active region, an ideal BJT transistor has a flat collector current response as the collector-emitter voltage changes. But in real devices, as you increase the collector-emitter voltage the collector current increases. This is generally modeled as a resistor across the collector-emitter junction in parallel with the basic small-signal equivalent circuit.

For an ancient transistor like the 2n2222, this output resistance is pretty low. How low is determined by the Early voltage and the nominal collector current a collector-emitter voltage of zero (obtained by projecting the sloped curve back to the y-axis. If you back-project that line further to where it crosses the x-axis (i.e., a collector current of zero), that crossing point is the negative of the Early voltage (for an NPN). In theory, for any base current, the resulting collector current line will back-trace to that same point. This is seldom true in practice, but it is close enough for most purposes. The smaller the Early voltage, the less the output resistance. Similarly, the greater the collector current, the less the output resistance.

As Jony130 discovered when he looked at the model used by MultiSim, it's Early voltage was only 10 V, which most of us think is a bit on the low side. But that might be a model for the early 2n2222 transistors and not the more recent versions such as the 2n2222A. The basic model included with LTSpice has an Early voltage of 100 V. That fact that both of these are round numbers indicates that not a lot of effort was made to determine really good values -- they are just rough approximations of where that mythical "typical" device lies.

So your calculation might be correct according to the model you used, but there's strong evidence that it is wrong because you didn't use a good enough model -- meaning that the 5 kΩ collector resistor you have results in the transistor's output resistance being too relevant to be ignored.

So what model should you use?

Ideally, you should use the model developed by the manufacturer of the device you are using. That's not always possible. The manufacturer may not make the models available (or you may not be able to figure out how to get them) or you may not even know who the manufacturer is.

But I would tend to trust a model from A manufacturer of that part over the model that comes for free with a simulator library (unless that library is vendor-specific, in which case it might be pretty trustworthy).

I just looked at ST Microelectronics website and they have a model file for the 2n2222AHR (their version of the 2n2222A, albeit one that is rad hard) and it has an early voltage of 50 V.

Take it for what it's worth -- but this drives home again the value of designing a circuit such that its performance is insensitive to what the Early voltage turns out to be for the particular device you happen to use.

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#### ericgibbs

Joined Jan 29, 2010
17,130
Does LTspice model use typical values ?
hi hero,
As you may have noticed, from previous posters, it depends on which version of the datasheet the person creating the transistor model used to get the parameters.

Also, there are variations in the stated parameters from one manufacturer to another.

Most simulators should only be used as a guide to check the 'approximate' performance of your design.

As you are beginning to learn, as engineers we all work in a 'World' of close approximations when designing all our projects.
You can do your maths calculations to the 'nth' degree, but it will not guarantee that the actual circuit will meet those calculations.

Most experienced design engineers are aware of the variation in device parameters, so they design their projects, so the variations in parameters will have a minimal effect on the circuit's required performance.

E

#### WBahn

Joined Mar 31, 2012
28,138
Now I'm confused between BF and beta, Hfe . Is it the same thing? In LTspice BF is 200 but Multisim is 153 first I think that BF is beta , Hfe and beta = Ic/Ib . Both of Multisim and LTspice , Ic and Ib are close therefore beta also are close but BF is different.
Does that mean beta and BF are different?
The generic "beta" of a transistor is a pretty non-specific ratio of collector current to base current. It tends to vary over a wide range of values, both for a given transistor as operating condition changes, and from one transistor to another.

h_FE is the large-signal (or DC) beta, which is the ratio of the total collector current to the total base current when the transistor is operated in the Forward current amplification mode in the common Emitter configuration (hence the F and the E in the subscript).

h_fe (note the lower case instead of the upper case) is the small-signal beta, which is the ratio of the change in collector current to the change in base current.

The small-signal and large-signal values are often close enough that the overall uncertainty in what a particular transistor's beta is makes the distinction irrelevant, but the small-signal beta tends to drop as the signal frequency increases, so for high frequency applications, the distinction becomes very relevant.

As an aside, is there a reason that you are using the ancient 2n2222? If you use a more modern transistor, even the still-old 2n3904, you can expect to find better models (and better performance).

Before you ask, don't ask what the best transistor to use is. Not only is the only truly defensible answer, "it depends,", but it is likely to start a religious war.

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#### WBahn

Joined Mar 31, 2012
28,138
@ericgibbs Does LTspice model use typical values ?
You can pretty much expect any generic model to depend on the "typical" device parameters. You can then go in and modify specific parameters within the model that you want based on your needs.

I don't know if these are available for discrete components, but models for designing integrated circuits often have what are known as "corner" models. For instance, is a CMOS process you might have five libraries, the typical and then four that comprise the combinations of slow and fast NFETs and PFETs. There might also be low- and high-temperature libraries that are specifically characterized at some low or high (the manufacturer defines what "low" and "high" means).

For IC device models, the fab models tend to be damn good -- if they are going to charge customers a million dollars to make a set of masks to produce a chip, those customers expect the actual device to perform extremely close to what the simulations show, since prototyping the circuit simply is not even remotely an option (other than buying space on a multi-project wafer run which is still going to cost you tens of thousands of dollars).

When I first starting in IC design, I took it on faith that the simulation results would only bear a passing similarity to the actual chip performance. I was shocked when I did my first lab test of one of our chips and found that the various bias voltages for the current mirrors varied from the simulation results by only a few millivolts.

Since the standard model definitions, by nature, lag way behind the need for more accurate models that take into account more things with greater fidelity, fab houses usually resort to implementing their device models as subcircuits using the existing simulation model definitions to capture the behavior. When I designed a chip on the IBM 130 nm process (when it was pretty new), I had reason to dig into the model file for some information and discovered that the model for an NFET was actually a subcircuit with over 300 devices in it. At least that explained why my simulations were so damn slow.

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#### LvW

Joined Jun 13, 2013
1,618
The small-signal and large-signal values are often close enough that the overall uncertainty in what a particular transistor's beta is makes the distinction irrelevant, but the small-signal beta tends to drop as the signal frequency increases, so for high frequency applications, the distinction because very relevant.
Yes, this is true - and this difference (and the associated tolerances) no longer matters at all when the transistor is operated in a circuit with negative feedback (which is practically always the case).

#### WBahn

Joined Mar 31, 2012
28,138
Yes, this is true - and this difference (and the associated tolerances) no longer matters at all when the transistor is operated in a circuit with negative feedback (which is practically always the case).
There's a limit to what negative feedback can do when the h_FE is 200 and the signal is at such high frequency that h_fe has dropped to 2.

#### Heroz

Joined May 29, 2022
31
The generic "beta" of a transistor is a pretty non-specific ratio of collector current to base current. It tends to vary over a wide range of values, both for a given transistor as operating condition changes, and from one transistor to another.

h_FE is the large-signal (or DC) beta, which is the ratio of the total collector current to the total base current when the transistor is operated in the Forward current amplification mode in the common Emitter configuration (hence the F and the E in the subscript).

h_fe (note the lower case instead of the upper case) is the small-signal beta, which is the ratio of the change in collector current to the change in base current.

The small-signal and large-signal values are often close enough that the overall uncertainty in what a particular transistor's beta is makes the distinction irrelevant, but the small-signal beta tends to drop as the signal frequency increases, so for high frequency applications, the distinction becomes very relevant.

As an aside, is there a reason that you are using the ancient 2n2222? If you use a more modern transistor, even the still-old 2n3904, you can expect to find better models (and better performance).

Before you ask, don't ask what the best transistor to use is. Not only is the only truly defensible answer, "it depends,", but it is likely to start a religious war.
Are beta and BF same thing?

#### LvW

Joined Jun 13, 2013
1,618
There's a limit to what negative feedback can do when the h_FE is 200 and the signal is at such high frequency that h_fe has dropped to 2.
Oh yes, of course. These feedback effects are relevant for a sufficiently large loop gain only.

#### Heroz

Joined May 29, 2022
31
To be able to answer this question I extract 2N2222 BJT's model from Multisim.

And if we do this, we see that Early's voltage (VAF) has a very low-value VAF = 10V. Thus, the transistor output resistance (ro) will be extremely low.

ro ≈ (11.3V + 10V)/3.73mA ≈ 5.7kΩ

Therefore the voltage gain will be around

Av ≈ (Rc||RL||ro)/re ≈ (5kΩ||5.7kΩ||100kΩ)/6.9Ω ≈ 2.6kΩ/6.9Ω ≈ 376V/V
Sorry I have a question. What is BF ?
In Multisim BF is 153 but LTspice is 200. Does this mean beta but why it is constant?

#### Jony130

Joined Feb 17, 2009
5,439
Sorry I have a question. What is BF ?
In Multisim BF is 153 but LTspice is 200. Does this mean beta but why it is constant?
BF is an Ideal maximum beta ( β, Hfe).
And Beta is not constant.

See yourself:
Multisim 2N2222

And LTspcie model

#### ericgibbs

Joined Jan 29, 2010
17,130
Yes!

#### MrChips

Joined Oct 2, 2009
28,095
For small signal design I never worry about the value of beta.
I assume that beta is higher than 100 and that is usually the case (more like 300).

For switching applications you assume beta to be between 10 and 20.