# Calculating dc gain of transistor

#### Man10

Joined Jul 31, 2018
90
I looked at the data sheet for tip110. According to 1 graph. The gain depends on temperature. It was a graph of collector current vs DC current gain. I saw three lines, 1 for 25 Celsius, 1 for -55 Celsius, 1 for 125 Celsius. What if the temperature is 10 Celsius, how do I calculate the gain?

#### KeithWalker

Joined Jul 10, 2017
1,778
How accurate do you need the result to be? You can extrapolate it from the data shown.

How accurate do you want the result to be? The relationship between gain and temperature appears to be fairly linear so you can extrapolate it from the curves shown. It will be about 1/8th. of the distance between the 25 Deg. and the -55 Deg. curves lower than the 25 Deg. curve . Those are only typical values, If you want it more accurately, measure it yourself. You really only need to measure it at the minimum and maximum collector currents for your application.

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#### ElectricSpidey

Joined Dec 2, 2017
1,653
I would just use the number for 25 Celsius, because a circuit shouldn't be that dependent on gain.

#### crutschow

Joined Mar 14, 2008
27,184
Such a value is only of academic interest.
Why do you need such a specific value of gain?
You always design a circuit to be largely independent of temperature.

#### Man10

Joined Jul 31, 2018
90
Such a value is only of academic interest.
Why do you need such a specific value of gain?
You always design a circuit to be largely independent of temperature.
So engineers design a circuit to be largely independent of temperature?

#### MrChips

Joined Oct 2, 2009
23,515
So engineers design a circuit to be largely independent of temperature?
Yes.

#### Man10

Joined Jul 31, 2018
90
How accurate do you need the result to be? You can extrapolate it from the data shown.

How accurate do you want the result to be? The relationship between gain and temperature appears to be fairly linear so you can extrapolate it from the curves shown. It will be about 1/8th. of the distance between the 25 Deg. and the -55 Deg. curves lower than the 25 Deg. curve . Those are only typical values, If you want it more accurately, measure it yourself. You really only need to measure it at the minimum and maximum collector currents for your application.
View attachment 238783
How do I extrapolate from the curves?

#### Audioguru again

Joined Oct 21, 2019
3,173
You are looking at the current gain, not the voltage gain.
The current gain is a range of numbers because each transistor is a little different and changes when the temperature changes.
As shown on the graph and text, the current gain also changes when the collector current changes.

A circuit uses some negative feedback to reduce the effect of variations of Vbe, hFE, temperature and current.

#### Man10

Joined Jul 31, 2018
90
So how do I design a transistor to be largely independent of temperature?

#### KeithWalker

Joined Jul 10, 2017
1,778
The vertical distance between the -55Deg. and the 25Deg. curves represents the difference of 80Deg.10Deg. is 15Deg lower than the 25Deg. So, at any collector current, the gain at 10 Deg.will be the gain at 25Deg.minus (15/80 times the difference in gain from -55Deg to 25Deg).

#### Papabravo

Joined Feb 24, 2006
16,103
So how do I design a transistor to be largely independent of temperature?
You use negative feedback to make the gain dependent on the external components in the circuit whose values can be tightly controlled and are less dependent on temperature. For example 1% resistors are now pretty much garden variety commodity components. There is no such thing as a transistor with a 1% gain characteristic. Capacitors come in many flavors and the X7R, NPO & COG varieties have much tighter tolerances than any semiconductor EVER made. So that is how you design circuits with semiconductor devices. BTW it is the same technique that was used with vacuum tubes and for the same reasons.

OTOH a transistor might have a DC current gain with of mean of 150, with a standard deviation of 25. If the current gain for this transistor was a normally distributed random variable, then 99% of all transistors manufactured would have a gain in the range [75,...,225]. That corresponds to ±3σ (± standard deviations) around the mean value. Can you see the problem with having a design that depends on the actual value of DC current gain.

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#### Man10

Joined Jul 31, 2018
90
So how should I calculate gain?
Give an example. Should I take temperature into account?

#### dl324

Joined Mar 30, 2015
12,871
So engineers design a circuit to be largely independent of temperature?
Yes. We use conservative numbers for beta so that variations with temperature don't affect circuit operation and we don't let the junction exceed the maximum recommended by the manufacturer (150C in this case).

The curves you referenced are for junction temperature, not ambient. Junction temperature is calculated using the appropriate thermal resistances and power dissipation.

#### dl324

Joined Mar 30, 2015
12,871
So how should I calculate gain?
Give an example. Should I take temperature into account?
Show us a schematic.

#### Man10

Joined Jul 31, 2018
90

Moderators note : reduced image to the essential part

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#### Papabravo

Joined Feb 24, 2006
16,103
So how should I calculate gain?
Give an example. Should I take temperature into account?
You should NEVER have to calculate the gain of a transistor. You must always calculate a range of gains for the final circuit based on a worst case analysis of the passive components that determine the gain,

#### Man10

Joined Jul 31, 2018
90
How do I calculate gain? Give me an example. Should I take temperature into account?

#### dl324

Joined Mar 30, 2015
12,871
The transistor is backwards, we need resistor values, and the circuit has no function other than to discharge the battery and heat up the transistor (and resistors).

#### Man10

Joined Jul 31, 2018
90
You should NEVER have to calculate the gain of a transistor. You must always calculate a range of gains for the final circuit based on a worst case analysis of the passive components that determine the gain,
I forget old information a lot and I find engineering projects really hard. I work hard to learn engineering a lot.

#### Papabravo

Joined Feb 24, 2006
16,103
I forget old information a lot and I find engineering projects really hard. I work hard to learn engineering a lot.
My solution to this problem is to take good notes that I can refer back to. Lately I have been using a simulator to take notes and pictures (schematics) at the same time. I now have, seven 3" Binders full of notes on various circuits, The zip file is in excess of 3 MB.