For the following circuit:



http://i1127.photobucket.com/albums/l637/hrstar24/th_circuit1.jpg

I need to find R1 so that Iz minimum is 5 mA under worst case load, power supply, and component tolerance. Vcc varies +- 10%, β for Q1 is typically 100, but has a min of 40 and a max of 300. VBE is .7 V, and for the zener diode rz = 6Ω, it has a 6.8 voltage drop at a test current of 5 mA. I already got Vzo also. I don't really know where to start.

So in worst case load, power, and tolerance, does that just mean Vcc = 10.8 V, β = 40, and IL is 0? Can I just ignore the BJT in this case? Also the next question asks me to find Iz maximum under worst case conditions, whats the difference between Iz min and Iz max?

 

This equation should do the work.

R1 = (Vcc_min - Vz) / ( Iz_min + Iload_max/β_min )

Vz = Iz_min * rz+Vzo

 

Thanks for the help. I am still a little confused about what the difference is between the Iz minimum and the Iz maximum however. To get the Iz maximum do you just set the load current to 0 and use the same equations?

Also, how would I go about calculating the output voltage Vo with both no load and with a 100 mA load? I know that Vb is just Vz, and Vout is Ve, so Vout = Vz - Vbe. With no load, do I just assume Ie = 0, so Ib = 0? Therefore Iz = current across R1?

 

Thanks for the help. I am still a little confused about what the difference is between the Iz minimum and the Iz maximum however. To get the Iz maximum do you just set the load current to 0 and use the same equations?

Look at the diagram

And from KVL we have
IR1 = Iz + Ib
So know it should be obvious that Iz_min occurs when Ib_max
And we have Ib_max when load is max and current gain of the BJT is min and Vcc_min.
We have similarly situation withe Iz_max
Iz_max occurs when Ib_min and Vcc_max

Also, how would I go about calculating the output voltage Vo with both no load and with a 100 mA load? I know that Vb is just Vz, and Vout is Ve, so Vout = Vz - Vbe. With no load, do I just assume Ie = 0, so Ib = 0? Therefore Iz = current across R1?

Withe no load you still have small current that is flow through R2.
And max current is flow through diode. So there will be max voltage drop across rz.
And when IL=max then Iz_min flow through diode, and this means smaller voltage drop across rz.
Vz = Iz * rz+Vzo

 

Ok thanks for clearing that up for me. How do I go about calculating IR2 when there is no load current? Is wasn't specified in the problem, so I can't use the general equation to find the collector current. Any hints?

 

I am guessing that Ib will be so small that it is negligable when I calculate Iz max. Is this correct?

With this, I get these 3 equations, where I can solve for IR1, Iz, and Vz:

IR1 = Iz
Vz = Vzo + rz*IR1
IR1 = (Vcc - Vz)/R1

Is this correct for calculating Iz max?

 

You got it almost right.
IR1 = (Vcc - Vzo)/ (R1+rz)