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# BJT Saturation Questions/Verification

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#### shimniok

##### Member
I've already Googled this topic and consulted my old EE text so I think I have the right info. I just wanted to run this by the gurus to 'check my work' and see if I am getting it or if I'm a dope. Also had a couple of questions about interpreting bits of a datasheet. Hope you can help.

No, this isn't homework. I got my BS in Comp Engr 16 years ago. (With more of a software focus, as you will no doubt be able to tell)

The goal is to understand BJT saturation and to design a simple circuit by selecting RB to ensure the BJT is in saturation with a decent overdrive factor. Eventually I will make this more complex and attempt to drive a small DC motor, but that's a long ways away. I'm just telling you that because you may wonder why I am using RM for the collector resistor rather than RC. M stands for motor even though it is a pretty poor approximation of a motor!

Here's the circuit.

Let's say that RM is given to be 18Ω and VCC is given to be 9V. So, I need to find an RB to drive the transistor into saturation.

My book (Microelectronic Circuits, Sedra & Smith) goes through a pretty simple process to make calculations for driving the transistor into saturation. Start by finding the maximum IB where the transistor is in active mode; set VCB = 0 and you get:

IC = (VCC - VB) ÷ Rm
= (9 - 0.7) ÷ 18 = 0.46A

This collector current is achieved by driving
IB = IC ÷ β

Question 1: β is the same as hFE for an IC of ≈.5A from the datasheet? (Looking at the ON Semi datasheet.

If so, then...

IB = 0.46 ÷ 100 = 4.6mA

As I understand it, the idea is that if we drive more than 4.6mA into the base, the transistor enters into saturation, with no significant (or, more to the point, no proportional) gain in IC. As you increase IB, β (well, the book calls it βforced) starts to fall.

The book talks about how, when driving more than the above IB into the transistor, the CB junction becomes forward biased at about 0.4-0.5V and as a result, VCE is around 0.2 to 0.3V. The book estimates VCE ≈ 0.3V for further calculation.

Question 2: The datasheet specifies a VCE under the "on characteristics" for various currents. Using a TIP3055, the datasheet says something like VCE=1.1V at IC=4A and VCE=3V at IC=10A. How does that relate to the above? Would I use these higher voltages to more accurately calculate for higher IC values?

Moving on, the next step is to figure out base saturation current:

ICsat = (VCC - VCEsat) ÷ RM
= (9 - 0.3) ÷ 18 = 480mA

Then

IBsat = ICsat ÷ β
= 480mA ÷ 100 (again using hFE at 0.5A from the datasheet)
= 4.8mA

Now, the book says to select IB = Overdrive-Factor • IBsat where the overdrive factor is 2-10, so sayeth Sedra and Smith. So...

IB = 10 × 4.8mA = 48mA

Finally we get to the point of selecting RB to ensure 48mA base current. The book uses 0.7 for VBE.

Question 3: The datasheet "On" characteristics shows VBE = 1.8V What is this? Should I be using 1.8V instead of 0.7V for VBE for saturation??

RB = (VCC - VBE) / IB
= (9 - 0.7) / .048
= 173Ω

When I turn around and run all this through SPICE*, the numbers** for IC, IB, VCE, and VBE all come out pretty close, actually. To the extent that I think the estimations for VCE and VBE must be "close enough".

In addition to the 3 questions... the final one is...

Question 4: does it sound like I am on the right track here? What am I missing? I'm probably still a dope no matter what but... did I goof up anything?

Michael

* SPICE deck; TIP3055 model comes right out of the data sheet:
-------8<----cut-here-----8<-------
Motor driver
V9 1 0 9.0
RM 1 3 18
VM 3 4 0
Q1 4 5 0 TIP3055
VB 6 5 0
RB 1 6 173

.MODEL TIP3055 NPN(Is=457.5f Xti=3 Eg=1.11 Vaf=50
+ Bf=156.7 Ise=1.346p Ne=1.34
+ Ikf=3.296 Xtb=2.2 Br=7.639 Isc=604.1f Nc=2.168
+ Ikr=8.131m Rc=91.29m Cjc=278.7p Mjc=.385 Vjc=.75
+ Fc=.5 Cje=433p Mje=.5 Vje=.75 Tr=1.412u Tf=37.34n
+ Itf=35.68 Xtf=1.163 Vtf=10 Rb=.1)
.control
op
print v(4) i(vm) v(5) i(vb)
.endc
.end

-------8<----cut-here-----8<-------

**SPICE results

MacSpice 86 -> source testA.cir

Circuit: Motor driver

v(4) = 1.175230e-01
i(vm) = 4.934709e-01
v(5) = 7.678676e-01
i(vb) = 4.758458e-02

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I think you're on the right track. Just keep in mind that if you're using hfe and VCB=0 to achieve saturation, that just barely gets you there. You'll need to provide more base drive to get further into the saturation region. Also, the figure for hfe can vary widely, use the minimum figure in your analysis. I think someone in here wrote that iB should be equal to iC/10 for saturation, and that sounds like a good place to start.

VCE is going to be affected by the collector current, and rise with rising current. Drive the base with more current as you requre more collector current. The figure VBE=1.8V wsa given for IC=4A. You're current isn't going anywhere near that much. You might be fine using VBE=.7V, but you'll just have to try it and see.

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Also... (BTW, I used that book in college too)

Now, the book says to select IB = Overdrive-Factor • IBsat where the overdrive factor is 2-10, so sayeth Sedra and Smith. So...

In saturation, the transistor is no longer a current source, so Bata is not a figure or merit. I think of the B-E as a simple diode in this case. I wouldn't fool around with overdrive factor.

The S&S text is really about micro-electronics. In power, there are some different ways of doing analysis.

Here is what LTSpice's built-in 3055 model predicts.

#### Attachments

• BaseResistor.jpg
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I think you're on the right track. Just keep in mind that if you're using hfe and VCB=0 to achieve saturation, that just barely gets you there. You'll need to provide more base drive to get further into the saturation region.

Understood -- do you think the 10x overdrive factor is enough here?

Also, the figure for hfe can vary widely, use the minimum figure in your analysis.

Ok, good info, thanks. I could use their low value of 20 which would result in higher Ib still.

I think someone in here wrote that iB should be equal to iC/10 for saturation, and that sounds like a good place to start.

That's basically what I did. Ib = 10 x Ic/β = Ic/10 in my case. Cool. [edit: of course for lower hfe, it's another story I suppose]

VCE is going to be affected by the collector current, and rise with rising current. Drive the base with more current as you requre more collector current. The figure VBE=1.8V wsa given for IC=4A. You're current isn't going anywhere near that much. You might be fine using VBE=.7V, but you'll just have to try it and see.

Ok, cool, thanks. It looks like, from the SPICE model, like it is in the ballpark (actually 0.77V). Eventually I'll breadboard it and see what I come up with for real. So, basically Vce has to do with voltage drop across the junction(s) which is ohmic in nature?

OutToLunch said:

Sure, eventually. I had some reasons to explore BJTs for now. I'll get there, don't worry.

Michael

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So, basically Vce has to do with voltage drop across the junction(s) which is ohmic in nature?

Vce has components of both resistance and a voltage barrier potential.

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Also... (BTW, I used that book in college too)

In saturation, the transistor is no longer a current source, so Bata is not a figure or merit. I think of the B-E as a simple diode in this case. I wouldn't fool around with overdrive factor.

I think that makes sense.

The way I read it, Beta is current gain and essentially current gain goes to crap once you enter saturation, so you're basically solving for Rb to where current gain is 1/10th what it would be in active mode... which essentially ensures you're into saturation to some degree... I *think* what I am saying here is essentially the same thing as what you said -- that Beta isn't a figure of merit in that you're beyond the point of using Ib to gain more collector current (ie, the transistor isn't a current controlled current source). You've basically maxed out Ic and you're just selecting a high Ib to ensure the transistor is really really honest-abe ON.

The S&S text is really about micro-electronics. In power, there are some different ways of doing analysis.

Any good books or websites I should check out? In the meanwhile I will see if Introduction To Circuits With Electronics: An Integrated Approach (Belanger, Adler, Rumin) has any additional light to shed...

Again, thanks all for the input/info so far, this is most helpful!

Any good books or websites I should check out?

From here on, it's "Burn and Learn"

The datasheet for every transistor lists its "max saturation voltage loss". Most are with the base current at 1/10th the collector current.
The 2N3055 and MJ2955 also show the max saturation voltage loss when the collector current is as high as 10A. Then the base current is 1/3rd of the collector current.

BTW, I was recently driving an ignition coil primary with a 2N3055. The collector current would rise lineraly from 0 to about 4 amps during the "On" cycle. I had to drive the base at a full amp to keep the device from popping out of saturation. That was Ic/4 at only 4A collector current!

Hi there,

Here is a graph of collector emitter voltage for four different collector
current levels (blue, 1, 2, 3, and 4 amps) for a sweeping base current
from 10ma to 500ma for the 2N3055 transistor.

To help understand saturation, we'll look at the graph for a collector
current of 4 amps. Note that the blue point marks 4 volts and about
250ma. This represents a gain of 16. The transistor is not in saturation
though and this is evident by noting that the collector emitter voltage
characteristic is roughly parallel to the Y axis. With increased base
current eventually the transistor starts to enter saturation, and this is
evident by noting where the voltage starts to curve drastically.
As the transistor enters farther into saturation, the collector emitter
voltage drops more and more, and eventually becomes roughly
parallel to the X axis. Note how the voltage characteristic changed
from roughly parallel to the Y axis to roughly parallel to the X axis
as the transistor enters saturation.
Note also that on the data sheet saturation isnt specified until
about 400ma of base current for 4 amps collector current, and note
that this represents a forced gain of only 10 now.
Thus, to ensure that the transistor is in saturation, the current has to
be significantly higher than the minimum gain which is spec'ed at
20 at 4v collector emitter voltage.

A good lab exercise is to wire the transistor up to a power supply or
two and vary the base current while trying to maintain collector current
just to see that at some point the voltage goes fairly low and then
after that sometime it does not decrease as significantly for increased
base current.
You could actually do this experiment and record the results, but there
is one more little thing to consider and that is temperature. You would
also want to vary the temperature to see how much the temperature
affects the saturation points. The key places to look are at the two
temperature extremes (highest and lowest that the application will
have to work in) and a few points in between too because the beta
often changes as a somewhat lopsided upside down parabola.

Note on the graph Vbe is also shown just for reference.
Also note that power dissipation is not shown and some of the
upper points on the graph may not be possible due to over heating.

Have fun and please let us know what results you get if you decide to
do this experiment. You'll have to record everything of course for
every point you wish to look at.

#### Attachments

• 2N3055-VceSat.gif
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Thanks all for the continued input/wisdom. Still thinking over some posts.

I may try the varying Ib experiment some day when I have time again (while I have time for keyboard use between feedings of new Baby Girl, I have no time in the garage to mess with circuits)

Meanwhile I tried modeling the circuit in SPICE with differrent Rb values from 10kΩ down to 10Ω (and hence different Ib values) to see what the outcome would be on Vce and Ic. Essentially doing my own version of the Ib vs Vce plots from MrAl and the Vbe/Vce/Ib lots from MikeMI (thanks for posting those!!) with Ic thrown in.

According to the results below, it seems clear to me that once Ib falls somewhere between 3 and 8mA that Vce stops decreasing so fast, and Ic stops increasing so fast. Vce really starts to level off between Ib=37mA and Ib=82mA. That all seems to check out with what everyone's been posting/plotting and what I've been reading / calculating.

--------------------------------------------------------------------------------
i(vb) v(4) i(vm)
--------------------------------------------------------------------------------
8.330635e-04 7.419989e+00 8.777837e-02
1.015237e-03 7.056072e+00 1.079960e-01
1.223469e-03 6.643573e+00 1.309126e-01
1.767888e-03 5.591050e+00 1.893861e-01
2.514860e-03 4.220833e+00 2.655093e-01
3.767076e-03 2.122792e+00 3.820671e-01
8.268636e-03 1.677621e-01 4.906799e-01
1.007868e-02 1.576338e-01 4.912426e-01
1.214807e-02 1.501479e-01 4.916585e-01
1.756000e-02 1.386067e-01 4.922996e-01
2.498786e-02 1.299220e-01 4.927821e-01
3.744299e-02 1.217240e-01 4.932376e-01
8.218698e-02 1.094158e-01 4.939213e-01
1.001608e-01 1.069385e-01 4.940590e-01
1.206994e-01 1.048157e-01 4.941769e-01
1.743592e-01 1.012360e-01 4.943758e-01
2.478827e-01 9.857571e-02 4.945236e-01
3.708538e-01 9.646707e-02 4.946407e-01
8.095428e-01 9.521620e-02 4.947102e-01

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Umm just a question, do you really need to use a 3055? They are designed to be driven from another transistor ie they are very low gain. The 3055 was just a cheap *final stage* transistor with reasonably high current and high dissipation.

These days there's almost certainly a better BJT for a single component motor driver. What's your motor current range and voltage?

Hi again,

Yes i agree that the 3055 isnt that great of a transistor, but it's well documented
so it makes a handy device to learn from.

Umm just a question, do you really need to use a 3055?

They are designed to be driven from another transistor ie they are very low gain. The 3055 was just a cheap *final stage* transistor with reasonably high current and high dissipation.

A very astute question -- I'm going to go with "no." The 3055 is probably overkill, sort of like swatting a fly with an h-bomb, in my case.

These days there's almost certainly a better BJT for a single component motor driver. What's your motor current range and voltage?

I'll let you know as soon as I find out. I basically pulled an unmarked motor so I'm not really sure about that particular motor. I may try to get some measurements (or I may just get another motor for which I can get a data sheet).

I suspect it is somewhere in the 300-800mA range for runtime with stall current around 1-2A judging by a Mabuchi motor of similar size / voltage range / rpm.

The motor doesn't need anywhere near the max capacity of a 3055. It was just a convenient power BJT that radio shack had in a pinch which was less likely to overheat than TO-92 packaged transistor.

So anyway, to find a better BJT, I'll start a new thread.

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