The Tachometer Circuit
The circuit that you are about to build is shown in the schematic above. Its purpose is to measure
the rotational speed of a shaft. The shaft might be the output of a motor or engine, so the
usefulness of this circuit for a mechanical engineer is obvious. At first glance, the circuit probably
looks confusing and overwhelming, but it can easily be divided into several modules whose function
is easy to understand. We will go through each module in order, and by the end of this document
you should have a good grasp on how the circuit operates.
On the simplest level, the circuit takes magnetic pulses in at one end, and generates a voltage (to be
measured with Arduino) at the other end. The voltage is proportional to the speed at which the
magnetic pulses arrive at the input. Thus, pulses that arrive in quick succession will generate a high
voltage, and vice versa. By calibrating each voltage with its corresponding shaft speed, we can create
a tachometer.
Magnetic Pickup
Differentiator
Rectifier
Pulse Generator
Lowpass filter
Signal Conditioning
The block diagram above shows the sequence that the signal passes through the circuit. At the
beginning, we have a magnetic pickup that detects the presence of a ferrous material. As one
“petal” of the daisywheel passes the pickup, its output voltage changes from high to low, then back
to high again. The signal conditioning circuitry changes the pulse into a “trigger” that is understood
by the pulse generator. When the pulse generator receives a trigger, it creates a pulse of an exact
duration. The lowpass filter “calculates” the average voltage that it sees - the more pulses it sees per
second, the higher the average voltage. The filter sends this averaged value to Arduino, where it can
be translated into a rotational speed.
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Magnetic Pickup
At the heart of the magnetic pickup circuit is the Melexis MLX90217 Hall Effect Geartooth Sensor.
It uses the Hall effect to detect changes in magnetic flux, as when a ferrous material is nearby.
N S
N S
Output = 0V
Output = 5V
The figure above shows a view of the sensor from the top. As you can see, a magnet has been glued
to the back of the sensor, and the magnetic field passes through to the front of the sensor. It is very
important that the south pole of the magnet be attached to the sensor - reversing the magnet will
prevent the sensor from detecting anything. When a ferrous object (such as one of the petals of the
daisywheel) is in front of the sensor, its output voltage goes to 0V (ground). When the petal moves
away, the sensor outputs the power supply voltage (5V, in this case).
The LED is used as an “idiot check”, just to make sure the sensor is working. When the sensor
detects the daisywheel, the lower leg of the LED goes to ground and the LED lights up. When
nothing is in front of the sensor, the lower leg of the LED is at 5V. When both legs of the LED are
at 5V, no current can flow and the LED remains dark.
The 300Ω resistor is used to limit the flow of current through the LED. Without it, the LED would
burn out in a matter of seconds. In general, there is a 2V voltage drop across the LED. Using
Ohm’s law, we find that
5V − 2V
= 0.01A
300Ω
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flows through the LED when lit. 10mA is a nice, safe current that will light up most LEDs.
A few other, minor details: R4 is in the circuit to ensure that the output of the pickup is 5V when
nothing is detected. You might think of the pickup as a switch. When it detects something ferrous, it
connects the output to ground, which is 0V. When it doesn’t detect anything, it disconnects the
switch. With no connection between output and ground, no current flows through R4 (or the LED,
either). With no current flowing through the resistor there is no voltage drop, so the lower leg of
the resistor is also at 5V. This is known as a pullup resistor and is very commonly used in the output
of sensors to ensure that they go “high” when nothing is happening. Without the pullup resistor,
the output would “float”; i.e. it could take on any value between 0 and 5V.
The 10μF and 10nF capacitors are used to smooth out the power supply voltage. This way, any
electromagnetic interference that is picked up by the wires leading to the tachometer won’t get
passed along to the signal. One really useful way to look at a capacitor is as a device that blocks low
frequency signals (and DC) and passes through high frequency signals. Since EMI is high frequency,
it will pass through the capacitors to ground, leaving the 5V supply line unaffected.
To summarize, the magnetic pickup circuit generates 0V when it detects the daisywheel petal, and
5V when it doesn’t. The result is a regular sequence of pulses (a square wave) whose frequency
depends upon the rotational speed of the daisywheel.
The Differentiator
The next few modules in the circuit transform the square wave into something that the pulse
generator can recognize. First, note that the pulse generator can only be triggered by a negative pulse
of very short duration. If a longer pulse is used to trigger the pulse generator, multiple output pulses
may result for a single input pulse. Thus, we need a way to shorten the pulses going into the pulse
generator - the shorter the better.
One simple way to do this is to differentiate the square wave, just like in calculus. In a square wave,
the signal is steady for a while at 0V, then makes an abrupt transition to 5V where it again remains
steady until it abruptly transitions back to 0V. The signal transitions from 0 to 5V in a very short
time, so the derivative of the signal is essentially infinite at the transitions. Conversely, the signal
remains constant between transitions, so its derivative is zero. The result of differentiating the
square wave is a series of positive and negative “spikes”, as shown in the figure above.
Constructing a differentiator is surprisingly easy, as you can see by the circuit above. Recall that the
capacitor allows high frequency (rapidly-changing) signals to pass through, but blocks low frequency
(steady, or slowly-changing) signals. The steady parts of the square wave are blocked, while the
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rapid transitions are passed through as spikes. R5 serves to pull up the output when nothing is
happening, in a similar manner to the pullup resistor earlier.
The Rectifier
The pulse generator is triggered by negative pulses, positive pulses will confuse the pulse generator or
even damage it. The purpose of the rectifier is to eliminate the positive pulses, allowing only the
negative pulses to pass through. A diode (shown as D1 in the figure) allows current to pass through
in only one direction. If the voltage on the left side of the diode is higher than that on the right, the
resulting current will be blocked by the diode. On the other hand, if the voltage on the left side is
more negative, the current will pass through unhindered (with a small voltage drop). Thus, the
diode blocks positive pulses, and allows negative pulses to pass through. If we wanted only positive
pulses, we would just reverse the orientation of the diode. As before, R7 acts as a pullup resistor to
keep the signal at 5V when nothing is happening.
The Pulse Generator
The pulse generator circuit is formed around an LM555 timer chip. The 555 is a classic chip, first
introduced in 1971, that is used in everything from timers to power supplies (and tachometers!)
More than 1 billion 555s are produced every year, despite the age of the design.
The 555 in the circuit above is configured as a “one-shot”. That is, it sends out a pulse of a precise
duration every time it receives a trigger signal. Once the pulse has been generated, the 555 does
nothing until it gets another trigger input. Thus, every time the 555 receives a trigger input, it
generates a pulse with a specified width. The square wave generated by the 555 timer is directly
related to the number of daisy wheel “petals” the hall-effect sensor detects. Below are sample pulse
trains generated by the 555 timer at different speeds.
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Low speed
Medium speed
High speed
According to the datasheet, the 555 can generate pulses anywhere from microseconds to hours in
duration! The duration of the pulse is determined by the values of R8 and C4 according to the
following equation
𝑇 = 1.1𝑅8 𝐶4
So now we must do a little math to determine the desired length for the pulses coming out of the
pulse generator for our daisy wheel setup and expected speed range. Let the number of slots in the
daisywheel be 𝑁𝑠 , and the speed of the rotating shaft be 𝑛. Then the time between pulses from the
daisywheel is
𝑇=
60
𝑛𝑁𝑠
where the 60 is used to convert from revolutions per minute to revolutions per second. For
example, if the shaft is rotating at 2000rpm and there are 6 slots in the daisywheel, then the time
between pulses is 5ms. If we were to incorrectly choose 𝑅8 and 𝐶4 , such that the 555 timer
produced a pulse width of 6ms, then more pulses would be received by the 555 timer than it could
produce. This means pulses from the generator will “overlap” each other and the output will remain
at a constant 5V, as shown in the figure below. Further increases in speed will not change the
output, and so our tachometer is useless at these high speeds.
Trigger Pulses
Output of Pulse Generator
Our goal, then, is to make the pulses from the pulse generator just wide enough to begin to overlap
at the maximum expected speed. You might wonder why we don’t just make the pulses really
narrow, so as to have an almost unlimited maximum speed. Recall that the next circuit in the chain
will take the average value of the output of the 555. If the pulses remain narrow regardless of speed,
the output voltage will stay very low and it will be tough for Arduino to make distinctions between
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speeds. For the best resolution, we’d like the maximum expected speed to correspond to 5V at the
output, with the minimum speed being somewhere around 0V. Thus, the pulses coming out of the
555 should be approximately equal to the time between pulses from the daisywheel at maximum
speed.
It is much easier to keep the capacitor value constant (since there is a much smaller variety of
capacitor values) and change the resistor to achieve the desired pulse length. The equation for the
proper resistor value (assuming that the output pulse and daisywheel pulse are set equal) is
60
= 𝑇 = 1.1𝑅8 𝐶4
𝑛𝑁𝑠
𝑅8 =
60
1.1𝑛𝑁𝑠 𝐶4
Thus, for 2000rpm and 6 slots, the correct resistor value is 20,661Ω. Of course, you won’t find a
resistor with exactly that value, but 20k is close enough. In our circuit, the pulse length is
𝑇 = 1.1 × 20kΩ × 220nF = 4.84ms
We would not want to round up to 22kΩ (the next available resistor), since it will produce a 555
timer pulse length of 5.32ms, and result in clipping at the higher end of the expected range.
𝑇 = 1.1 × 22kΩ × 220nF = 5.32ms
V
t
The Lowpass Filter
The final stage in the circuit is the lowpass filter. The lowpass filter removes any high frequency
content from the signal (the pulses) and passes along low frequency (and DC) signals. For our
circuit, the lowpass filter passes along the average value of the voltage coming into it. If the pulses
are close together, the average voltage is high, and if the pulses are widely spaced, the average value
is low. The lowpass filter has a cutoff frequency given by
𝑓𝑐 =
1
= 1.59Hz
2𝜋𝑅6 𝐶5
This means that the filter blocks anything above 1.59Hz, and allows anything below 1.59Hz to pass
through. As with everything electronic, this circuit design is a tradeoff. If we make the cutoff
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frequency very low, it will make the output signal nice and smooth, but will be very sluggish in
responding to changes in speed. If we make it very high, much of the choppy nature of the pulses
will be passed through, and it will be hard for Arduino to measure the speed correctly. The 1.59Hz
represents a tradeoff between smoothness and response time.
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