# Input Impedance for a 2N2222A NPN transistor

#### NaV007

Joined Oct 16, 2019
2
Why is it that there is a Max and Min rating for the input impedance (h_ie) in the datasheet of a 2N2222A NPN transistor? The datasheet for reference(https://www.st.com/resource/en/datasheet/cd00003223.pdf). Why is the impedance not fixed at one value? And if someone is designing a circuit which value is to be considered? Any help is greatly appreciated.

#### ci139

Joined Jul 11, 2016
1,696
if you see other conditions for this test it becomes more obvious
Code:
hie Input Impedance Min/Max/Unit
IC = 1. mA VCE=10V 2.00 8.00 kΩ
IC = 10 mA VCE=10V 0.25 1.25 kΩ
they pass certain current through CE
which is likely done by pulling V.E down by certain value relative to V.B

& impedance = that they likely vary the base voltage a bit and
check for input impedance e.g. R=dU/dI
where dU is V.B variation and dI is related I.B change ... Fig.2 for h11 / hfe

there likely are special conditions how to bias the measurement circuit
and i hope thy sample the current going to and voltage at Base terminal
but the point is that
the junction response
depends
(also and) on Ic (collector current)

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#### drc_567

Joined Dec 29, 2008
1,093
Impedance is defined as the ratio of voltage divided by current. If you were to devise a means to measure the input current to the transistor, possibly with a low value series resistor placed at the base terminal, then you could measure the input impedance using the ratio V/I.

#### Papabravo

Joined Feb 24, 2006
15,730
Why is it that there is a Max and Min rating for the input impedance (h_ie) in the datasheet of a 2N2222A NPN transistor? The datasheet for reference(https://www.st.com/resource/en/datasheet/cd00003223.pdf). Why is the impedance not fixed at one value? And if someone is designing a circuit which value is to be considered? Any help is greatly appreciated.
Because manufacturing processes do not work the way you want them to. For every parameter there will be a range of acceptable values. The range represents the ±3σ points on a normal distribution bell curve. What that means is there is a small probability, less than 1%, that a device could have a value outside that range. What is a designer to do you say? Glad you asked. The answer is that a design should not depend on the particular value of a device parameter. Given the vast number of successful designs over the last century, that seems like a reasonable solution.

#### WBahn

Joined Mar 31, 2012
26,398
Why is it that there is a Max and Min rating for the input impedance (h_ie) in the datasheet of a 2N2222A NPN transistor? The datasheet for reference(https://www.st.com/resource/en/datasheet/cd00003223.pdf). Why is the impedance not fixed at one value? And if someone is designing a circuit which value is to be considered? Any help is greatly appreciated.
In general, the input impedance depends on the operating point of the transistor. The data sheet values are for specified operating conditions. Production process variations make it impossible to fix any parameter at one value -- there will always be a tolerance. The tighter you want that tolerance, the more you will pay for the part. If you are designing a circuit that requires a specific value in order to function properly, you have a poor design. You need to design your circuit so that it can operate properly over a range of parameters wider than the process variations of the parts you are using. The wider your allowable range, the greater the selection of components are that you can choose from.

#### MrAl

Joined Jun 17, 2014
8,136
Why is it that there is a Max and Min rating for the input impedance (h_ie) in the datasheet of a 2N2222A NPN transistor? The datasheet for reference(https://www.st.com/resource/en/datasheet/cd00003223.pdf). Why is the impedance not fixed at one value? And if someone is designing a circuit which value is to be considered? Any help is greatly appreciated.
Hi, and welcome to the forum.

There's a very simple explanation for that. The input voltage to a transistor is not linear with current, or you could say that the current is not linear with the voltage. This makes the resistive part of the input impedance vary with different currents.
A regular resistor has simple formula:
R=V/I
where 'V' is the voltage and 'I' is the current and so as the voltage changes by a factor 'a' the current changes by that same factor 'a'.
In a non linear device like a diode or transistor base emitter diode, this relationship changes. A rough simplified formula for a particular diode would be like so:
i=1e-9*(e^(19/V)-1)
and so the resistance would be:
R=1e9*V/e^(19/V-1)

and you can see right off that it is a very different kind of relationship between current and voltage and so a very different resistance.
With a regular resistor you get a graph that is a straight line but with a diode you get a curve with a sharp "knee' where it looks like the leg of someone sitting in a chair. Thus the resistance on one side of the knee is very different from that of the other side, and it actually varies throughout the entire range of input.

#### WBahn

Joined Mar 31, 2012
26,398
Hi, and welcome to the forum.

There's a very simple explanation for that. The input voltage to a transistor is not linear with current, or you could say that the current is not linear with the voltage. This makes the resistive part of the input impedance vary with different currents.
That's a different issue. The question was why was there a Min and a Max. Since those parameters are at specified operating conditions, the fact that the response is nonlinear doesn't matter because the operating conditions for which those min and max values apply are fixed.

#### MrAl

Joined Jun 17, 2014
8,136
Hi,

I think that view is a little extreme though.

"Why is it that there is a Max and Min rating for the input impedance (h_ie) in the datasheet of a 2N2222A NPN transistor? The datasheet for reference(https://www.st.com/resource/en/datasheet/cd00003223.pdf). Why is the impedance not fixed at one value? And if someone is designing a circuit which value is to be considered? Any help is greatly appreciated."

With attention to:
"Why is the impedance not fixed at one value? Any help is greatly appreciated."

Clearly the non linearity is part of understanding why the impedance is not fixed even if process variation is also a factor. Process variation is also a good point though because with a variation in chemical composition we see a similar difference.
Also, "Any" is another key word. Even if the above wasnt true, it's darn good to know.

Stated another way, the difference in impedance due to process variation could be either mitigated by the current induced impedance difference or it could be compounded so it is a good idea to know that angle too.

#### MrAl

Joined Jun 17, 2014
8,136
Another interesting fact i think is that if we look at the hFE we find that in the process variation we see a small increase in Beta for the change of collector current over a 10 to 1 range, which means at 10ma we need more input current relative to the Beta and thus higher up on the 'diode' current curve.
If we saw a linear change in Beta we'd have the same input voltage for 1ma as 10ma strange as that sounds which would mean it would look like a pure resistance, but we dont have that it's much different.
I'll post some numbers if i get a chance today so we can take a better look at this relationship.

#### MrAl

Joined Jun 17, 2014
8,136
Hi,

What do you want us to look at?
Nice graphs which help a lot but it would also help if you mentioned what point your graphs were trying to show.

#### Bordodynov

Joined May 20, 2015
2,834
First of all, I wanted to show that when the Input Resistance is considered, it is necessary to use a low signal gain. Second, I wanted to show you (not at two points) how the input impedance depends on current.
The low signal gain is not equal to the static gain. More precisely, they are only equal at one point. At low currents, the dynamic coefficient is greater than the static one, but at high currents, the opposite is true.
I gave an example of how to read the input impedance.
It is not correct to use a static gain for this purpose. For the spice-model I used, the maximum gain is 10 mA and therefore the dynamic and static coefficients are equal at this single point. And the resistance calculation (by schoolboy method) at a current of 10 mA may be correct by chance. At a current of 1 mA, the school method will give an underestimated input impedance. I can continue to prove it. If it is interesting.

#### MrAl

Joined Jun 17, 2014
8,136
First of all, I wanted to show that when the Input Resistance is considered, it is necessary to use a low signal gain. Second, I wanted to show you (not at two points) how the input impedance depends on current.
The low signal gain is not equal to the static gain. More precisely, they are only equal at one point. At low currents, the dynamic coefficient is greater than the static one, but at high currents, the opposite is true.
I gave an example of how to read the input impedance.
It is not correct to use a static gain for this purpose. For the spice-model I used, the maximum gain is 10 mA and therefore the dynamic and static coefficients are equal at this single point. And the resistance calculation (by schoolboy method) at a current of 10 mA may be correct by chance. At a current of 1 mA, the school method will give an underestimated input impedance. I can continue to prove it. If it is interesting.
Hi again,

Oh ok that is a clear and concise explanation thanks.

What i was looking at was the more theoretical end of it. When i look at the Beta spread for any collector current when we go up in collector current we only go up slightly in Beta, so we necessarily have to input more current not just because we wanted to raise the collector current but because the gain suffers more at higher currents. This in turn leads to a higher base emitter voltage and so the non linearity of the input resistance becomes more apparent.
The expressions that came out of it were like this:
[(B+3)/2, 1/2]
where the first entry is the base emitter voltage, and the second entry is the theoretical base current.
Most notable is that the base current can be held constant yet with change of Beta (due to process control) the base emitter voltage rises or gets lower (to maintain that base current level) thus inducing an input resistance that changes with Beta and the Beta change is of course very non linear too.
Note that is with a very precise circuit made up of a current source and resistors and a few voltage sources in order to control the experiment better.

#### BobaMosfet

Joined Jul 1, 2009
1,629
Impedance is defined as the ratio of voltage divided by current. If you were to devise a means to measure the input current to the transistor, possibly with a low value series resistor placed at the base terminal, then you could measure the input impedance using the ratio V/I.
Adding to this for noobs- Notice the first sentence..... you can see it in Ohm's law as: Z = E/I

#### Bordodynov

Joined May 20, 2015
2,834
When the input resistance is talked about, the dynamic resistance Rd=dVin/dIin is meant. This is not a static resistance Rst=Vin/Iin. In this case, Vin=Vbe and Iin=ib.

#### NaV007

Joined Oct 16, 2019
2
Thanks to everyone who gave their input! So my understanding of the input resistance is as follows-> It is a dynamic resistance due to production process variations and the exponential nature of the current. Hence it cannot be fixed at a value (@Bordodynov, @Papabravo and @MrAl). As a designer, one should be focused on making the circuit work for all those values (@WBahn). Thanks again to everyone who contributed!

#### Danko

Joined Nov 22, 2017
1,066
Why is it that there is a Max and Min rating for the input impedance (h_ie) in the datasheet of a 2N2222A NPN transistor?
Max and Min rating for the input impedance (h_ie) correlated with Max and Min rating for the DC current gain (h_FE).
For standard (fixed) collector current (I_c=1mA for example) base current depends on DC current gain.
So, with lower DC current gain, required base current is big and input impedance is low.
With higher DC current gain, required base current is low and input impedance is high.

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#### MrAl

Joined Jun 17, 2014
8,136
Max and Min rating for the input impedance (h_ie) correlated with Max and Min rating for the DC current gain (h_FE).
For standard (fixed) collector current (I_c=1mA for example) base current depends on DC current gain.
So, with lower DC current gain, required base current is big and input impedance is low.
With higher DC current gain, required base current is low and input impedance is high.
Hi

That is the point i was making too.

#### Bordodynov

Joined May 20, 2015
2,834
See

#### MrAl

Joined Jun 17, 2014
8,136
Hi,

I just have to say, that is a very nicely presented post.
If you are making a point with that you may wish to state that too even right in the same post.
Either way though, very nicely presented.