 ### Network # Designing Relaxation Oscillator

#### bonbonbaron

Sep 11, 2015
16
I'm learning how to design circuits from scratch. Yes, I know there are lots of ready-made plug-in kits out there, and a lot of rules-of-thumb for which resistor values to use with which components... But I want to understand circuit design from the ground up. That way I can build freely.

I'm analyzing a relaxation oscillator. I'm going to put an LED at Vout (it's rated for 30mA forward current and 3.0-3.6V forward voltage). Now, assuming +V is 6V, I want to figure out what all my other elements should be if I want the LED to blink at a frequency of 2Hz with a duty cycle of 50%.

What's the general method for designing a circuit like this? And does there come a point when a desired circuit gets too complex to design on paper? If so, then what's the general methodology for designing circuits in a simulator like MATLAB's Simulink?

(Please assume that I know Kirchhoff's Laws and how all the components work. And I'm not asking for what this specific circuit's elements should be-- I'm asking how you figure that out.) Thanks!
3B

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#### BobK

Jan 5, 2010
7,682
Ah, the old UJT. Haven't used one in about 50 years.

Do you understand how this circuit behaves? If so, please describe it. Then tell us where you think you might place the LED. Then we can talk about how to control the timing and the current through the LED.

Is that what you are asking for?

Bob

#### bonbonbaron

Sep 11, 2015
16
No, BobK, I'm asking how to solve for the values of the elements. But I'll answer your question anyway, because I think that's where you're going with this.

Here's my rough take on it: The input voltage first charges the capacitor. While it's doing so, it's powering Vout. Eventually the capacitor has a high enough charge to repel enough electrons into the transistor's base terminal to turn the transistor "on". THEN the input current is mostly shunted through the transistor's emitter and collector terminals, Vout is now at a lower voltage, and the capacitor discharges its electrons through the base and replenishes electrons on its other plate. Once the capacitor charge is insufficient to keep the transistor on, the cycle repeats.

I would place the LED between Vout and ground.

If I'm wrong in any way, please correct me. I'm here to learn.

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#### BobK

Jan 5, 2010
7,682
That is a pretty good explanation, but I would stay away from electrons doing this or that. We abstract electron behavior into voltages and currents, think in terms of those. We don't care what the actual electrons are doing.

When you say solve for the elements, that is ambiguous. You can use many different values of Rt C, Rb1 and Rb2. And the circuit will do something, probably oscillate at some frequency with some current flow through the resistors. Do you have an idea of what period you want for the oscillator and how much current you want to flow through the LED?

Bob

#### bonbonbaron

Sep 11, 2015
16
Thanks Bob.

I'm shooting for a period of 0.5 seconds. Since the LED's rated for 30mA forward current,,. I believe it's safer to go for about 50% of that. So around 15mA for LED current.

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,508
there are 2 voltages to consider. the first is the one where the ujt turns on, the second where it turns off. you have correctly identified that it turns on at a higher value than it turns off.

there are two current paths to consider. the first is the one which charges the capacitor, the second the one which discharges it. does one have to carry a larger current? why? what is the max current? what imposes this limit?

there are 2 time periods to consider. charge and discharge? given the two currents defined above, what are the actual charge and discharge currents, and how do we calculate the time period?

#### hevans1944

##### Hop - AC8NS
Jun 21, 2012
4,792
This website has a pretty good explanation of UJT operation.

If you load Vout with an LED, the timing will be affected.

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#### bonbonbaron

Sep 11, 2015
16
Hi everyone, I'm back. Had a busy past few weeks, and now I'm back to this puzzle. Right now I'm only concerned about how long it takes for the NPN BJT's base-emitter voltage to reach 0.7V (assuming that's how much turns it on).

So I took a deep breath and jotted down the system of equations (the below voltage loop equations are labeled with roman numerals, current node equations are labeled with capital letters). After the equations I'll define the terms, and I'll repost the image of the circuit to save you from scrolling yourself dizzy. (I) Vin - Rt*It - Vout = 0
(II) Vin - R2*I2 - Vcb - Rt*It = 0
(III) Vc - Vout = 0
(IV) Vc - Vbe - R1*I1 = 0

(A) Iin - It - I2 = 0
(B) It - Iout - Ibc - Ic = 0
(C) I1 + Ic + Iout - Ignd = 0
(D) I1 - I2 - Ibe = 0

DEFINITIONS (for terms not obvious from picture):

• Vc: voltage across capacitor
• Vcb: voltage of collector-base junction
• Vbe: voltage of base-emitter junction
• Ignd: current flowing to ground
• Ibe: current from base to emitter of NPN transistor (assuming I replace the UJT with an NPN BJT whose required base-emitter voltage for switching on is 0.7V)
• Ic: current "through" capacitor
• Vin: 9V battery
• Vout: LED rated at 3.3V and 15mA

ASSUMPTION FOR CAPACITOR'S CHARGING PHASE: I2 = 0, and thus V2 = 0 (is this correct for charging phase?). I1 will be small at first from the current flowing through the base-emitter junction.

REQUIREMENTS:
1. LED (Vout) must blink at 1Hz and 50% duty factor. (Looks to me like this oscillator design will produce a triangle wave though-- no matter. Assume I'm happy with the fade-in effect throughout the charging phase if that's the case.)
2. See LED and battery specs in the definitions.

I leave all the constants (resistor and capacitor values) unknown, as deciding what those should be is the whole point of all this. I've heard of RC as a time constant based on the solution to the differential equation of an RC circuit, but I'd like to see how the solution plays out here before blindly following that rule.

I've gotten as far as getting a set of 8 equations all in terms of Vout and/or Iout. However, it's not clear to me what to do from this point. If someone would kindly walk me through this problem, I will be eternally grateful. (And no this is not for school, so don't worry about helping someone cheat. In fact, feel free to leave a hint instead of an answer if that eases the burden on your conscience.)

If I've left out anything or made any errors in my problem setup, please let me know. Thank you.

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Moderator
Jan 21, 2010
25,508
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