Here is the crux of my problem:
Transistor as a Switch Example No2
Again using the same values, find the minimum Base current required to turn the transistor “fully-ON” (saturated) for a load that requires 200mA of current when the input voltage is increased to 5.0V. Also calculate the new value of Rb.

Transistor Base current:

Ib=Ic/beta

Transistor Base resistance:

Rb= (Vin-Vbe)/Ib

Transistor switches are used for a wide variety of applications such as interfacing large current or high voltage devices like motors, relays or lamps to low voltage digital IC’s or logic gates like AND gates or OR gates.

Here, the output from a digital logic gate is only +5v but the device to be controlled may require a 12 or even 24 volts supply. Or the load such as a DC Motor may need to have its speed controlled using a series of pulses (Pulse Width Modulation). transistor switches will allow us to do this faster and more easily than with conventional mechanical switches.


HOW CAN THIS BE VALID WHEN THE BETA IS VARIED?

For a switching application such as this, you design the circuit so that you force the beta to be about what you want it to be.

When the transistor is saturated, the Vce is very low -- in many cases you can just assume that it is zero. You calculate how much collector current there will be if this is the case (in your case, it is given as 200 mA).

In order to drive the transistor into saturation, you supply lots of base current. How much? It depends on the transistor (the data sheet is your friend), but for small-signal transistors the rule of thumb is 10% of the collector current.

You rely on the fact that the Vbe is fairly constant in order to choose a base resistor that will establish the desired base current.

 

Ib=Ic/beta
. . . . . . . .
HOW CAN THIS BE VALID WHEN THE BETA IS VARIED?

If you put in formula "10" instead "beta"
Ib=Ic/10
then beta of real saturated transistor automatically becomes 10
and its value is not varied.
See this diagram.

 

You are posting example questions taken from text books on how transistors work. Textbooks often use theoretical scenarios but often fail to show actual practical applications.

In your example, a transistor might show hFE = 300. However, this is for a given collector current Ic.
hFE will be different at a different Ic.

Let us look at the datasheet of a common transistor 2N2222.
View attachment 293524
You will notice that hFE values shown are minimum specifications.
Thus at Ic = 150mA, we can use hFE = 50 in our example question.
In a real world application, you want to derate this even further. The rule of thumb for switching applications is to use hFE = 10.
In practice, hFE in the range 10-20 is usually adequate.

Now that’s solved my question. I guess when you have just 2 ranges (min and max) you should interpolate the hfe for Ic? Also, datasheets have been a recurring problem for me. Can you recommend any good books or other that could educate me about them further? Much appreciated!

 

Now that’s solved my question. I guess when you have just 2 ranges (min and max) you should interpolate the hfe for Ic? Also, datasheets have been a recurring problem for me. Can you recommend any good books or other that could educate me about them further? Much appreciated!

Interpolating would be the wrong engineering approach.

If hFE is quoted as min 50, it means that all devices are guaranteed to function if you assume hFE to be 50.
It does not guarantee that the device will function correctly if you happen to assume hFE = 60.

 

Now that’s solved my question. I guess when you have just 2 ranges (min and max) you should interpolate the hfe for Ic? Also, datasheets have been a recurring problem for me. Can you recommend any good books or other that could educate me about them further? Much appreciated!

No. In a career that lasted over half a century I've never seen a cogent explanation of how datasheets are written or how they should be interpreted. The most useful concepts have come from classes I took in probability, statistics and random variables. In such classes you learn how physical quantities can be modeled by a probability distribution and what it means for you to have confidence that a part selected at random will meet certain conditions.

 

Now that’s solved my question. I guess when you have just 2 ranges (min and max) you should interpolate the hfe for Ic? Also, datasheets have been a recurring problem for me. Can you recommend any good books or other that could educate me about them further? Much appreciated!

More commonly you have a typical and a min. Usually you will only see a max value for one or two operating points (if any).

For most transistor circuits (there are certainly exceptions), you want to design to the minimum value, since higher values usually just mean better-than-designed performance.

The key is to ask yourself, "If I design this for a beta of 200 and it turns out the transistor I plug in only has a beta of 100, will the circuit performance still be acceptable?"

That goes both ways, of course. "If I design this for a beta of 100 and it turns out the transistor I plug in has a beta of 300, will the circuit performance still be acceptable?"

You want your circuit performance to be acceptable over the entire range of beta values that a particular transistor might have.

 

Ib=Ic/10
then beta of real saturated transistor automatically becomes 10

To perhaps clarify, that's called a "forced beta", which is used for design purposes when using the transistor as a switch.
It's not its actual beta, which is not measured under saturated conductions, but measured in the linear region with a collector-source voltage of several volts, well above its saturated voltage.

 

Go back to the plots in post #4 and you will observe:

1. There is a maximum collector current Ic(Q1) of 160 mA determined by the 30Ω resistor and the minimum collector emitter voltage of 0.2V.
2. No matter how much current is injected into the base V(c) will never be less than 0.2V
3. You can drive the "forced" beta lower than a value of 10, but there is little or no point in doing that

 

To perhaps clarify, that's called a "forced beta", which is used for design purposes when using the transistor as a switch.
It's not its actual beta, which is not measured under saturated conductions, but measured in the linear region with a collector-source voltage of several volts, well above its saturated voltage.

Called it "forced" or not, it is simple beta, by definition:
beta=Ic/Ib
It should be not messed with differential beta:
beta_diff=ΔIc/ΔIb
For example, beta_diff≈0,0355 at Ib=16 мА in circuit, post #4 :

 

Called it "forced" or not, it is simple beta, by definition:
beta=Ic/Ib

I disagree.
"Simple" beta is not defined in saturation.
"Forced beta" is the common name given to the base current used to place a transistor in complete saturation.
If Ic does not vary with a change in Ib, than that's not simple beta.

It should be not messed with differential beta:
beta_diff=ΔIc/ΔIb

Where does that come from, as I have never seen that stated on a data sheet?
Beta is normally defined in the data sheet as the collector current divided by the base current at a fixed Vce.

 

To me, saturation means you are getting as much collector current as possible for the circuit. Further increases in base current will have little effect on the collector current. So the differential beta approaches zero as we enter saturation mode.

 

Go back to the plots in post #4 and you will observe:

1. There is a maximum collector current Ic(Q1) of 160 mA determined by the 30Ω resistor and the minimum collector emitter voltage of 0.2V.
2. No matter how much current is injected into the base V(c) will never be less than 0.2V
3. You can drive the "forced" beta lower than a value of 10, but there is little or no point in doing that

I think about it much simpler.
With beta=10 transistor in my example has very low current gain=beta_diff=0,0355,
so dependence Ic on Ib changes is negligible, therefore working point is stable.

 

I quite often had a mental block when it came to reading transistor datasheets with all the numbers, abbreviations and calculating the base resistor of a transistor to saturate and switch the transistor hard on.
Then I found this website which helped me...
Transistor Base Resistor Calculator
....and basically 'ignored' the hFE values shown on the datasheets but used a forced beta of between 10 and 20.

I wanted to calculate ohm value of the base resistor (Rb in the picture below) to saturate a 2N2222 transistor so that while using an OpAmp on a 12vDC supply which the OpAmp gave an output of about 10v (Vi ) to switch on a 12vDC (Vcc), 400Ω (RL), 0.03A/30mA (iL) relay.

I now use a Forced Beta (hFE) of usually 10,
(Increasing the Forced Beta will increase the base resistor value)


With the 12v relay being RL = 400Ω, Vcc = 12v, and Vi (output of OpAmp) = 10v
The base resistor on this site is calculated as 3333.33Ω
...and also assuming that the saturation voltage of the transistor (Vbe) is 0.7v.

iL = Vcc / RL
= 12v / 400Ω
= 0.03A or 30mA
So Rb = Vi x Forced Beta / iL
= 10v x 10 / 0.03A
= 100 / 0.03A = 3333.33 Ω (3.3kΩ)

 

Your calculation of 3kΩ is correct.
This suggests that a base resistor of 1-3kΩ will be fine.

 

I think about it much simpler.

I believe you are the only one that thinks that way.

 

I think Danko is only looking at the datasheet graphs that show a "typical" transistor's specs. Then many of his projects will not work or will work poorly with all the transistors with minimum spec'd beta. Using a forced beta of 10 to saturate a little transistor (a huge 2N3055 has a recommended forced beta of only 3 at 10A) guarantees all of them will saturate well.

 

I think Danko is only looking at the datasheet graphs that show a "typical" transistor's specs. Then many of his projects will not work or will work poorly with all the transistors with minimum spec'd beta. Using a forced beta of 10 to saturate a little transistor (a huge 2N3055 has a recommended forced beta of only 3 at 10A) guarantees all of them will saturate well.

I think we are mostly all smart enough to realize that this is a cheap shot for purposes that are not manifestly obvious. It really is beneath you.