Well, I never thought about that that way! I never thought to do the math work on units too!

Anyway, I understand what you just said! But mathematically, where am I wrong? I mean, if that were just numbers with no electrical meaning, that math was correct, no?

I mean, if I have:

x² = y² / z
√(x²) = √(y²) / √z
x = y / √z

this is correct, no?

Yes, that math is correct. The numerical part you got was correct according to the messed up equation that you started with. But I think you are now starting to see that tracking units involves treating them as part of the value and doing all the math on them as well. This is very good.

 

Ok, forget it... That was just some unexplainable stupidity...

I was doing some messed up math...

I < P
(Vin - Vz) / R < V*I

This is non-sense!

Forget it!

Yep. We all get too lost in manipulating equations that we often miss mistakes because we don't ask if the units will work out. The habit you want to get into is looking at your work every few lines (every line during particularly hard parts) making sure that the units on every term are working out like they should. You will be surprised how many mistakes you will catch almost immediately after making them, how much LESS time you will spend on doing the work overall, and how much more correct your final results will be on average.

 

Morning...

Ok, after all that, I'm getting back to the problem focus!

The previous question is answered with that formula Iz_min < Rz < Iz_max, that turned out 159.2 Ω < R < 538.1 Ω.

Now the next question is to evaluate the dissipated power on both T1 and T2 transistors. To do this I need to find Vce1, Vce2, Ic1 and Ic2.

For Vce2 and Ic2, I think it's easier!

Ve2 = V_RL
Vc2 = Vin
so,
Vce2 = Vin - V_RL = 12 V - 4.2 V = 7.8 V

Ie2 = I_RL = Ic * ( (β+1) / β)
Ic2 = I_RL / ( (β+1) / β)
Ic2 = 420 mA / (31/30) = 406.5 mA

P2 = Vce2 * Ic2 = 7.8 V * 406.5 mA = 3.17 W (wow, bum)


For T1 I have:

Vce1 = Vcb1 + Vbe1

Vcb1 = Vc1 - Vb1 = Vin - Vz = 12 V - 5.6 V = 6.4 V

Vce1 = Vcb1 + Vbe1 = 6.4 V + 0.7 V = 7.1 V

Ib2 = Ie2 / (β\(_{2}\)+1)
Ie1 = Ic1 * ( (β\(_{1}\)+1) / β\(_{1}\))

Ie1 = Ib2



So,

P1 = Vce1 * Ic1 = 7.1 V * 13.41 mA = 95 mW

 

P2_max = (Vin_max - Vout_min)*ILmax = (12V - 4.2V)*4.2V/10Ω = 3.276W
P1 ≈ P2/β2 ≅ 3.276W/30 = 0.1092W = 109.2mW

 

P2_max = (Vin_max - Vout_min)*ILmax = (12V - 4.2V)*4.2V/10Ω = 3.276W
P1 ≈ P2/β2 ≅ 3.276W/30 = 0.1092W = 109.2mW

Well, for P2, the values are kinda matching. They are different by 3.35% ((3.17 / 3.28)*100).
For P1, they are different by 13% ((95 / 109.2)*100)...

Are my calcs correct or did I messed up somehow? Why do we have these differences?

 

If you assume that Pd = Vce * Ic, then your calculation are ok. But in general case Pd = Vbe * Ib + Vce * Ic.

 

If you assume that Pd = Vce * Ic, then your calculation are ok. But in general case Pd = Vbe * Ib + Vce * Ic.

Hum, ok... But you named the load current as IL max? And also Vout_min??? Shouldn't V_out be always 4.2 V???

 

In your idealized case (Ideal Zener diode and Vbe is constant) Vout is always equal to 4.2V.

 

@Jony130 , one last question!

If you assume that Pd = Vce * Ic, then your calculation are ok. But in general case Pd = Vbe * Ib + Vce * Ic.

And have you had that general equation into account in your calcs in your post #64?

 

No. But I show you how we "normally" do it.

 

Ok. Thanks!