DS0 Quad (DS0203) Oscilloscope - First Time Use

As a gift I received a new portable oscilloscope: the DS0203. This, I know will come in handy in the future! Nevertheless, there are a few things to note with its use... First and foremost, this may or may not be able to measure signals faster than 8MHz - I haven't tested anything high than 100KHz yet. Second and more importantly, there is a bit of a learning curve to it's use, something I wish to clear up here.


When I turned the device on, the first question I asked was: "How do I measure a signal?"

For this tutorial, you will need:

• DS0203 Oscilloscope
• Probe
• Signal Source (I used an Arduino UNO and generated a PWM wave on pin 9)

1. Plug one of the probes into CH-A
1. Attach the alligator clip to GND (ground)
2. Mount the probe to the signal source (pin 9)
3. (optional) See that the probe is set to "X10"
2. Turn on the DS0203 Oscilloscope
1. The power switch should be on the lower right
3. Press the "Play/Pause" button until the screen reads "RUN" in the upper left-hand corner (RUN will continuously capture a signal from the source, while HOLD will allow you to analyze the recorded signal before it changes)
4. Adjust the settings to improve the signal quality on-screen (Use the leftmost -...+ control to set the value and the rightmost -...+ control to navigate. Use the △ button to switch between horizontal and vertical menus.)
1. Under channel A (blue), set the values to 0.2V DC. This will vertically scale the signal on screen
1. Move the leftmost -...+  left or right to change 1V to 0.2V
2. Press the leftmost -...+ button to switch to signal type and change it to DC
2. Where it says "AUTO" (orange), set the time measure to about 500uS. This will horizontally scale the signal on screen
1. Move the leftmost -...+ left or right to change the time to 500uS
3. Set the threshold "THR" to stabilize the signal and reduce flickering
1. Press the △ button to navigate the menu on the right
2. Navigate to THR and press the leftmost -...+ button to select channel A (blue)
3. Then move the leftmost -...+ left or right to adjust the threshold (left moves down, right moves up; the threshold marker will be label 'T' on the left of the graph)
5. By now, a fairly decent wave should appear on screen. (These are the exact steps I used when familiarizing my self with the DS0203's environment)

Multi-Rotor Propeller Thrust Formulas

During the construction of my unmanned aerial vehicle (AUV), I needed to know how much thrust my motors would produce, or more, how much mass they could support. The objective is to optimize the mass to thrust ratio using differentiation. After about two hours of research and assistance, I found the formula for thrust, the relation to how much mass the given thrust can support. Next, a friend of mine demonstrated how to solve for air velocity before knowing the math by using the second method of solving a system of equations.

Thrust:

According to AirWolf II, "A commonly used rule is that velocity of the air at the propeller is v=½Δv of the total change in air velocity."

Where,

T	Thrust which is a kind of force (F).
D	The diameter of the propeller (m)
ρ	Air density - approximately 1.225 kg / m3
v	The velocity of the air pulled into the propeller (m/s)
Δv	The velocity of the air pushed away from the propeller (m/s)

Next, we can relate mass to the thrust by substituting T with the function for force (Force = mass (m) x acceleration (a)) and solve for m, giving us:

In order to find mass, we need to first know Δv - this is what slowed me down for a little while. So, in order to solve for Δv without first knowing the mass, we'll need to create a second equation (power = force x velocity):

Where,

η	Efficiency of motor (approximately .75)
W	The max wattage of the motor (W = IV or W = I2r  or  W = V2/r)
C	The scaling factor from 0 to 1 (one being maximum throttle)
m	Mass (g)
a	Acceleration
Δv	The velocity of the air pushed away from the propeller

Substitute and solve for Δv:

Then to solve for mass given thrust, simply plug Δv into one of the above formulas and vuala, mass is related to thrust and can be adjusted by either the power of the motors or the size of the propellers:

A real-world example using this formula:
I have brushless motors that run with a max current of 10.5A at 11.1V with a prop radius of 4.5" (0.1143m). Given the following:

C: 100%	η: 80%
ρ: 1.225 kg/m3	D: 0.2286 m
a: 9.8 m/s2	W: 116.55

...each motor with it's mounted prop running at 80% efficiency and the throttle maxed, can carry a maximum approximate weight of 615 grams (or 0.614646... kg). Since I have 6 mounted to my chassis, my AUV will be able to support a maximum [hover] load of approximately 3.69kg. (since the motors are arranged in pairs, this number may be further increased via an increase in efficiency by re-evaluating for v given the previous solved equation)