Impedance!

Sounds kinda like Impudence!
I have an exciting announcement to make, that has nothing to do with class, but what would a blog be without boasting about personal issues?

I GOT INTO MIT!!! Yay!! Which is extra cool since I have no background in engineering, and still got into the best (or one of) Aerospace Engineering program in the Country!!  In case you didn't know I am deciding between MIT and Cornell, so if anyone has insider information on who's better feel free to leave a comment!

So back to impedance.... another word for resistance.  All instruments have inherent impedance, no matter how much money you throw at it., so we had an activity to try to measure the impedance of our oscilloscopes. (which apparently have a capacitor and resistor in parallel)
At 100Hz, I calculated a Thevinin resistance of 1MegaOhm in the oscilloscope.
At 10kHz, the resistance fell to 140k.  I was going to figure out a way to solve for R&C using these data points when I realized I could look back at the filter lab we did earlier.  I found the frequency (2.5kHz) at which the voltage recorded by the oscilloscope dropped to 0.7, the f3dB!  Which should equal 1/(2pi*RC). Using this, I solved for RC (6.3x10^-5) and plugged this into the equation for resistors in parallel [R1R2/(R1+R2)]=Rthevinin.  Simplified with a cap in it Rth = [R/(wCR +1)]  which would be R / (really really small number + 1) --> R.
So R ~ 1Megaohm and C ~ 63 pico Farads

Diodes!!

I think diodes are really neat! They let current through one way, but not the other.  Basically a one way gate. Ideally, the diode would start to transmit as soon as the voltage is positive, but in real life, they have a small lag, ~0.6V for regular, 2.2 for red LEDs.  They can also be thought of as resistors, which are either infinity resistant (at negative V) or basically 0 at positive V.
  . I tried Measuring the resistance of a 1N914 diode, and got 5.30Mohm one direction and an error the other direction, as in too large to measure.

Other Neat things that you can do with Diodes are fiddling with sine waves!

Lab 3-2, we made "Half Wave Rectifiers", which basically blocked the negative side of a sine wave, from an wall-outlet. Apparently some cheapo companies will consider this DC, since it never goes negative.  The Blue is the full sine wave and Yellow is the rectifier.. As you can see, there is a little discrepancy from the height of the blue and yellow, that's because of the unideal nature of the diode, if you look closely, the yellow is 0.6V bellow the blue.  Pretty Neat huh?

We basically just kept adding elements to the original circuit to make new and exciting things.  If you add a Capacitor, then the signal starts to look like a pretty flat line! Getting pretty close to DC!

This Cap is 47uF, coupled with the 2.2k resistor, which is Red Red Red :)

give you an RC value of 0.1, which is much greater than 1/60 seconds so the Cap doesn't discharge much between peaks at 60Hz, which makes little ripples in the signal.  We can calculate the ripple amplitude using :

 So ripple amp = 0.16*Vmax. Vmax = ~10V (see the graph?)
dV = 1.6Volts.  If you look in the graph (the big boxes are 5V) you can see the ripple dip by 1.3 or so, which is pretty close, given the printed values on electronics can vary by 20%


Lab 3-5: Signal Diode / Rectified differentiator.

This one is like the differnetiator plus a capacitor.  If you look, you can kind of see that the yellow looks like a derivative of the blue line, if you only plotted the areas of positive slope.  The second picture is the same circuit without a 2.2k resistor load at the end, which basically altered the RC so now you can see the discharge signal amplified.

Lab 3-6: Diode Clamp


This circuit can be used to 'clamp' the voltage.  Basically trim the max output: I calculated the dynamic resistance of the diode, without the voltage divider, and got 250 Ohms.  With the full circuit set up, the capacitor is acting with a very low resistance at the sine frequency, thus making the voltage low and clamping the output.

Lab 3-7: Diode Limiter
You can use two diodes in opposite directions to let through and still limit both sides of the signal! This would be very useful for sensitive electronics that would be fried by high voltage!

"Blocking Capacitors"

Suppose you have TWO voltage sources...
How would you know which one wins? Or what the voltage at point A would be??  At first glance it may look like it should just be 10 since that's the difference in potentials... But no, it's more complicated (such is life).  You need to figure out what the current in the wire is, which is controlled by the resistance in you batteries.  Turns out the side with less resistance is has the more dominate signal.
You can also apply this idea to alter the output of a function generator.  Say you want to add an offset to a sine wave.  If you connect it to another power source (with a resistor so you don't loose the sine signal), the function generator would win, but if you add a capacitor, then the resistance on the function generator goes to infinity at for DC (0Hz) frequencies, and the alternate power source wins, and you get your offset!

Completed Lab 2-8. 

The Garbage Detector!

One of the cool things about electricity is that it is all around us, we use it pretty much for everything in our lives.  And the cool thing about studying it, is that we get to know more intimately how this crazy phenomenon works. This time, we got to look at what comes out of the outlet in the wall.  Of course we had a transformer, so we weren't in danger of electrocution, but it was as direct a sampling as we could get.

Transformer is attached to wall

Wired through capacitor and resistor

We ran the power through a simple circuit and were then able to see all the craziness that comes out through the power lines!

And signal looks like this!!

The Blue in the picture is the raw input, and the yellow is the signal ran through a high pass filter... As you can see there is a lot of higher frequency stuff added onto the regular 60Hz power supply!


Q/A : The attenuation here is 0.06 between the blue and yellow 60Hz signals

Capacitors Continued

So turns out that capacitors are really just like resistors that depend on the frequency of the signal fed to them.  A circuit with a resistor then capacitor will act like a voltage divider, so the "integrator" that I build last time will function if 1/wC << R, or when frequency >> 1/RC.
If we switch the Resistor and the Capacitor.... We get a "differentiator"! Math with circuits! who knew?
The "integrator" has another function, it can be used as a low pass filter ['low' frequencies are allowed to 'pass' through], since Vout = Vin *( 1/wc) / (R + 1/wc).  Consequently, the differentiator can also be used as a filter, but a high pass one. 


Questions for "Tuesday Feb 12th"

Lab 2‐2 in the Student Manual (An RC differentiator, experimentally)
   R = 1/wC = 1/(100kHz)(100pF)  = 100k
   Impedance at f = 0? R = infinity.  Impedance at f= infinity?  R = 0
Lab 2-4  Lowpass Filters
   f3dB Experimental = 1.2kHz; f3db Theoretical = 1.06kHz.  
   Phase shift at f3dB = -45degrees;  f << f3db = 0 degrees; f  >> f3db = -90 degrees
   Attenuation: 2f3db = 0.45; 4f3db = 0.25; 10f3db = 0.1.

Lab for "Friday Feb 15th"
Lab 2-5 Highpass Filters
    f3db = 1.2kHz again.
    Phase shift at f3dB = +45degrees;  f << f3db = +90 degrees; f  >> f3db = 0 degrees

Capacitors

Capacitors are kind of weird... they are like mini storage tanks for charge, and like resistors that change over time.  The capacitance (C) is equal to the charge built up over voltage.
Here's a very useful schematic from "The Art of Electronics Student Manual"

Using the following mathematics,

we basically proved that a circuit using a only a capacitor and resistor can be used as an "integrator" (which is way cooler than what your TI-83 graphing calculator can do), as long as V-out stays small. I used a function generator, to create various Vin signals (left), 
which I ran through my "integrator" (right) 

sine wave: 


square wave: 

triangle wave: 
 

  Pretty Neat Huh?


Lab / Questions for "Tuesday 12th" on capacitors:
Lab 2­‐1 in the Student Manual (An RC circuit, experimentally)
   500 kHz square wave, time for output to drop 37% =100 mirco seconds
    time for output to rise 63% 100 micro seconds.  R=10k, C=.01uF, RC = 1x10^-4 = 100us Works!

Build a "Cap-meter" with picoblocks program
 My cap-meter caps / outputs
1 x 0.1uF capacitor  ===  11
2 x 0.1uF in parallel ===  22
2 x 0.1uF in  series  ===  5
In parrallel the capacitors have to charge one after the other, but in parallel, the current can travel the path of least resistance.  The results make sense.

Transistors!

Way back when, the only way to turn something on and off was with a physical switch, which are prone to failure, until transistors came around!  Transistors are like mini switches that can be turned on by adding a very small charge.
The type of transistor we used was the MOSFET.  To be honest, I had a bit of trouble wiring up the transistor, when I was a kid, we would just stick things together and see how they worked, no fancy transistors, or even resistors... I got it working eventually, and used it to turn on and off a Lego motor.

questions for "Tuesday Feb 12th"

⌘ With the LEGO motor wired as above (powered by a battery and controled by the logo), program the LogoChip to turn the motor on and off. Use an oscilloscope to monitor the LogoChip output pin. Does the LogoChip have any trouble controlling the motor? Feel much torque it takes to stall the motor.
     . It actually works quite well like this, compared to wiring it directly to the logo
Attach another battery pack:  Wow it's really strong now

Voltage Dividers

Over the last couple classes, we also looked further into voltage dividers.  I figure it is important enough of a topic to get its own post. 

 

In this case the voltage supplied by the battery (V in) is decreased when you measure voltage over an individual resistor (V out). 

V out = V in * R2 / (R1 + R2)

"Thevenin's Good Idea"

A man named Thevenin once had a good idea. This idea was that If you had any collection of resistors, batteries, and diodes hidden in a box, one could replace it with a single batters and resistor, and the two would be indistinguishable, as far as voltage, current and resistance go, I'm sure the complex one would be heavier ;). I drew up a little diagram in gimp to demonstrate this.  So basically, you can replace any complex circuit  with it's "Thevinin equivalent".  And that was the topic of lab on Feb 5th.



Lab/Question for "Friday Feb 2nd": To test Thevinin, we used a LEGO motor. (Note dates may not match)
Fell the torque of the motor with a batterypack versus the logo-chip.
   .  The power from logo-chip is much weaker than the batterys.

⌘ Use an oscilloscope to monitor the change in the voltage p between the power and ground busses as you connect and disconnect a 47 ohm resistor between the busses. Based on your observations, (approximately) what is the Thevenin equivalent circuit for your battery pack?
   .  Vth = 4.5V  Rth = ~0

⌘ Use PicoBlocks to set one of the LogoChip output pins “high”. Use an oscilloscope to monitor the change in the voltage between this pin and ground as you connect and disconnect a 47 ohm resistor. Based on your observations, (approximately) what is the Thevenin equivalent circuit for the LogoChip output pin?
    .  Vth = 4.1V  Rth = 11.4

⌘ Based on your observations above and perhaps additional experiments, determine the Thevenin equivalent circuit for a non-spinning3 LEGO motor. How much current really flows into a motor driven by LogoChip pin?
    . [Motor and battery] Vth = 4.5V  Rth = 21.    I[Logo] =  Vlogo / (Rlogo + Rmotor) = 0.12 A

Lab 1-4 in the Student Manual:
    .  Vin = 4.5; Vout = 2.2; Isc = 0.43mA;  Vth = 2.2V; Rth = 5.1k
"Tuesday Feb 5th":
Lab 1-5 in the Student Manual (More with the digital oscilloscopes)
    .  Rise time of SquareWave =35 ns
Lab 1-6 in the Student Manual (AC Voltage Divider, experimentally)
    .  Vin = 200 mV   Vout = 100 mV

Week 1

 Finished the first week of class!
This week we learned how to make simple circuits with a breadboard, and no it's not made out of bread!
We get to play with picoblocks, a coding program for little kids.  Below you can see a pic of the bread board, which currently has a photo cell on it, attached to an oscilloscope.  See the little waves on the screen?  That's the florescent light flickering! The Lights have gotten a lot better since I was a kid, but they can't fool the photocell!!

Here are a few questions about the lab, I will keep them at the bottom of each post, so I don't bore the passerby.

Tuesday Jan 29th:

How much current flows in the circuit if R =1 kΩ?

   . V of a battery = 4.5V and if R=1000 Ohms, I =V/R = 4.5 mA

Can you tell by looking at it if current is flowing in the circuit?

   . No

How much current flows through the LED?

   . The voltage across a Red LED is 2.2V for the light to turn on, so the voltage across the resistor is 2.3, 

      and I must be 23 mA

If you double the current by cutting R in half, does the LED “look twice as bright?” Why not?

   . No, the LED is basically either on or off, the 'brightness' only changes if you vary the frequency of on/off

Do the readings change in the way you expect as you cast a shadow on the photocell?

     . Well they do decrease, I couldn't get it to go to zero though

⌘ Can you make a shadow detector? That is, can you make the LED flash whenever your hand casts a shadow on the photocell?  Yes. It was neat.

Hiya Everybody!! This is my first attempt to make a blog by myself! Woohoo! Come and journey with me through an exciting semester of...

 "Techniques for Experimentalists, Physics 210"

Where I learn about how to do physics and play with circuits and expensive machinery!