# Gas station without pumps

## 2017 June 25

### Fidget spinners revisited

Filed under: Uncategorized — gasstationwithoutpumps @ 17:55
Tags: , , ,

In Fidget spinners, I wrote about measuring and modeling the acceleration of two fidget spinners, 5-spoke spinner that cost $6.90 made from plastic and brass and a 3-bladed spinner that cost$8.90 milled out of brass:

The 5-spoked wheel spinner weighs 32.88±0.03g, and the 3-spoke brass spinner weighs 61.14±0.02g.

The previous post looked only at the fidget spinners spinning vertically (that is, with a horizontal axis), but I had noticed in playing with the spinners that they seemed to have different drag in different orientations, so I redid the measurements with the spinners horizontal (that is, with a vertical axis). I had a somewhat harder time spinning the spinners fast with them horizontally mounted, as my makeshift support for the photointerrupter was a bit precarious.

The 5-spoke wheel seemed to run smoothly , but the fit suggests more dry friction and less fluid friction.

The 3-spoke spinner really does not like to spin horizontally.

To visualize the physics better, I tried making acceleration vs. velocity plots for the fitted models:

When holding the wheel horizontally, there seems to be mainly dry friction, almost independent of the speed of the spin.

The 3-spoke spinner has much worse drag at all speeds when held horizontally rather than vertically. The fluid drag seems to be about the same as before, but there is much larger dry friction component (possibly from brass-on-brass contact between the spinner and the axle caps).

As expected from fidgeting with the spinners, the 3-blade spinner has much more drag than the wheel, both horizontally and vertically. The change from mainly wet friction to mainly dry friction for the wheel was unexpected, though.

Update 2017 Jun 25 21:15:  My wife just pointed me to a Wired article: https://www.wired.com/2017/05/the-phyiscs-of-fidget-spinners/ which does a poorer job of the same thing I did. They sampled at a fixed rate, rather than recording time stamps on each rising edge, so they had much poorer time resolution, and they assumed constant acceleration (dry friction), which is only appropriate for low-quality bearings.

## 2017 June 23

### Uncompensated transimpedance amplifier

Filed under: Circuits course — gasstationwithoutpumps @ 16:07

In my book Applied Electronics for Bioengineers, I have students build transimpedance amplifiers for phototransistors (and some students use them for electret microphones as well).  In the book, I never deal with compensating the transimpedance amplifiers to avoid oscillation, as I try to stay away from students having to reason about phase of signals and oscillation has never been a problem in the student designs.

But I thought that I ought to understand the method myself, especially if I need to help students trying to do higher bandwidth, higher gain transimpedance amplifiers.  First I read up on the subject—one of the better introductions is the Maxim application note 5129 Stabilize your transimpedance amplifier.  The key concepts are the following:

• When the frequency is high enough (where the open-loop gain is limited by the gain-bandwidth product) the phase change of the amplifier is about –90° (or 90° for the negative input).
• If we set up a transimpedance amplifier with feedback resistor R, then the feedback consists of a low-pass RC filter: a voltage divider with R on tap and the input capacitance of the amplifier and any capacitance in parallel with the current source on the bottom.
• The phase change of a low-pass RC filter (gain $\frac{1}{1+j\omega RC}$) approaches –90° above the corner frequency.
• Having a phase change of 0° and gain ≥ 1 around a feedback loop results in instability and possible oscillation.

That means that we can have instability at frequencies between $\frac{1}{2\pi RC}$ and the gain-bandwidth product (though we probably only have problems for frequencies at least a factor of 3 above the low-pass corner frequency, since the phase change of the filter is only asymptotically –90°).  If the parasitic capacitances are low and we only request small transimpedance gain, then RC is small, and the corner frequency of the low-pass filter is above the gain-bandwidth product, so there are no problems.  Will the students ever encounter problems?

Today I tried to make an unstable transimpedance amplifier using the MCP6004 op amps that we use in class.  The op amps have a gain-bandwidth product of 1MHz, so I needed an RC time constant much larger than 160ns.  I chose 2MΩ and 47nF for an RC time constant of 94 ms and a corner frequency of 1.69Hz.

The very large bypass capacitors are to make sure that there are no sneak paths through the power supply and positive input—to make sure that I’m looking at the phenomenon I’m really interested in.

I connected the amplifier up to the Analog Discovery 2, and I definitely got instability:

There does seem to be a somewhat unstable oscillation happening.

The reasoning about the amplifier instability suggests that the oscillation should be at about the frequency where the gain around the loop is 1, that is where $\frac{f_{GBW}}{f}\frac{1}{2\pi f RC}=1$ or $f= \sqrt{\frac{f_{GBW}}{2\pi RC}}$. For the circuit I made, that would be around $\sqrt{1MHz \; 1.69Hz}= 1.3kHz$.

I did some FFTs of the waveform (averaging over hundreds of traces to reduce noise, since the signal is fluctuating).

The peak is around 1380Hz, very close to the predicted oscillation frequency. Also visible are harmonics of 60Hz, which are the correct output of the transimpedance amplifier (picking up stray currents by capacitive coupling).

To compensate a transimpedance amplifier, we need to add a small capacitor in parallel with the feedback resistor, making the gain of the feedback filter $\frac{1+j\omega R_{F}C_{F}}{1+j\omega R_{F}(C_{F}+C_{i})}$, where $R_{F}$ and $C_{F}$ are the feedback components and $C_{i}$ is the input capacitance. For “optimal” compensation, we want to set the upper corner frequency $1/(2\pi R_{F}C_{F})$ at the geometric mean of the lower corner frequency $1/(2\pi R_{F}(C_{F} + C_{i}))$ and the gain-bandwidth product $f_{GBW}$. Using a larger capacitor (overcompensating) increases the phase margin (thus allowing for some variation from specs) at the cost of reducing the bandwidth of the final amplifier.

We can set the equation up as $1/(2\pi R_{F}C_{F})^2 = f_{GBW}/(2\pi R_{F}(C_{F} + C_{i}))$, which we can simplify by assuming that $C_{i} \gg C_{F}$ to get $C_{F} = \sqrt{ \frac{C_{i}}{2 \pi R_{F}f_{GBW}}}$, which for my design comes to 61pF.

A 68pF compensation capacitor cuts out the oscillation peak, but there is still a fair amount of noise around the corner frequency of the amplifier (1.2kHz). Overcompensating with a 680pF capacitor reduces the noise substantially, but the bandwidth is reduced to 120Hz.

I also tried a somewhat more realistic example, with only a 2.2nF input capacitance, which calls for about a 13pF compensation capacitor. A 20pF capacitor does fine:

The oscillation is well suppressed by the compensation capacitor.

Now I have to decide how much (if any) of this to include in my book. Perhaps it can be an optional “advanced” section in the transimpedance amplifier chapter?

## 2017 June 20

### Fidget spinners

Filed under: Uncategorized — gasstationwithoutpumps @ 17:34
Tags: , , ,

I recently bought two fidget spinners from Elecrow:

The 5-spoked wheel spinner weighs 32.88±0.03g, and the 3-spoke brass spinner weighs 61.14±0.02g.

The heavier 3-bladed spinner cost $8.90 and is milled out of brass (though the site claims “pure copper”, the material looks like brass and is slightly magnetic, so I’m sure it is brass).The lighter 5-spoke spinner cost$6.90.

The lighter spinner is easier to get to high speed, spins longer, has more gyroscopic effect, and has a dimple for balancing it on a pencil point, so makes the better fidget spinner in many ways.

I was curious whether I could characterize the fidget spinners electronically. I have a photointerrupter (an aligned LED and photodetector) from Sparkfun with a 1cm gap that the spinners just fit in.

Here is the 3-spoke spinner mounted in the Panavise Jr, with the photointerrupter counting 6 ticks per revolution.

Here is the 5-spoke spinner with the photointerrupter counting 5 ticks per revolution.

I set up PteroDAQ to record a timestamp on every rising edge of the photodetector, which counts 5 uniformly spaced ticks per revolution for the 5-spoke wheel, but 6 ticks (in 3 pair of closely spaced ones) for the 3-bladed spinner. I can then plot the angular position of the spinner as a function of time in gnuplot:

# The Galaxy LED Spinner!

We are excited to announce the Galaxy LED Fidget Spinner! The Galaxy is the highest quality LED spinner in the world.

Here’s some feature bullet points in no particular order:

• Three minute plus spin time
• 3 High-quality micro-lights
• New Design
• 14 Different Flashing Patterns
• 4x Beautiful Color Sets for each Flashing Pattern
• Demo mode that switches the pattern every 12 seconds
• Battery lock so you don’t worry about it turning on in your pocket
• The light is equally visible from both sides
• High quality hybrid ceramic bearings
• Easy battery replacement
• 15 hours of battery life
• Ability to flip lights in opposite directions for different light trail effects
• Held together by strong neodymium magnets for easy and repeatable assembly
• And more…