Symbol in circuit analysis I don't know/understand

[six el six]

What are the two parallel vertical lines I see in Merlin's books?

They look like this:

Zout = Ra ll ra
   
In the above example they're the lines in between the Ra and the ra.

If there's a link somone could give me that would be swell.

Or just an explanation.

As always thanks,
six

[John]

|| means paralleled.

[PRR]

100K||60K == 37.5K

[Willabe]

Zout = Ra ll ra

OK, after seeing PRR's post I just noticed it's written Ra || ra and not Ra || Ra.  And PRR wrote 100K || 60K = =37.5K.

So to take it a little further, 3 questions.

1. Is there a difference between writing Ra and ra or is it the same meaning? Is it OT R (Ra) and anode/plate R (ra) on 1 side of a P/P output stage?
2. I thought it meant resistance anode to anode? Where did you get 100K || 60K?

3. Why double = = ?


                 Brad        

 

[John]

Well I hope this is right or else I have to un-learn what I think I know. 

Ra means the plate resistor you are using. ra means the plate resistance that is listed on the datasheet. For instance, on the sheet I have for a 12ax7 ra is approx 62500 ohms.

The plate resistor appears in parallel with the anode resistance in the tube (??? I think that's how it works ???) I don't have my head around why it works that way yet. I have yet to  design a stage with a certain gain in mind, I just copy from different schematics and see what sound I like.

[Willabe]

Thanks John.


               Brad     

[six el six]

Very helpful replies.

Danke!

[HotBluePlates]

The plate resistor appears in parallel with the anode resistance in the tube (??? I think that's how it works ???) I don't have my head around why it works that way yet.

Imagine you are an electron sitting at the plate of the tube. You're looking for a path to ground. You look one way, and see the plate load resistor (Ra); the other way, you see the internal resistance of the tube (ra). The plate load resistor looks like a path to ground if you're part of an a.c. signal, because on the other end of it is a filter cap, which looks to you like a short-circuit to ground. In other words, for a.c., it is the same as ground.

If you want to describe the output impedance of the tube, you account for not only the plate load resistor, but also the parallel path to ground through the tube's internal resistance. Hence Zo = Ra ll ra, because the two paths look the same as two parallel resistors between the plate output and ground.

[John]

That is a great explanation!! Thanks very much.

[six el six]

If you want to describe the output impedance of the tube, you account for not only the plate load resistor, but also the parallel path to ground through the tube's internal resistance. Hence Zo = Ra ll ra, because the two paths look the same as two parallel resistors between the plate output and ground.

Ok. I understand that one of the paths to ground is through the plate load resistor to the + side of a filter cap.

But what direction is the parallel path to ground through the "tube's internal resistance" taking?

[sluckey]

Refer to the pic...

1. Blue is the path thru the plate resistor.
2. Red is the path thru the tube (plate to cathode) and the cathode resistor.
3. Green is the path thru the external load.

All three paths are in parallel.