The personal website of Scott W Harden

# Exponential Fit with Python

Fitting an exponential curve to data is a common task and in this example we'll use Python and SciPy to determine parameters for a curve fitted to arbitrary X/Y points. You can follow along using the fit.ipynb Jupyter notebook.

``````import numpy as np
import scipy.optimize
import matplotlib.pyplot as plt

xs = np.arange(12) + 7
ys = np.array([304.08994, 229.13878, 173.71886, 135.75499,
111.096794, 94.25109, 81.55578, 71.30187,
62.146603, 54.212032, 49.20715, 46.765743])

plt.plot(xs, ys, '.')
plt.title("Original Data")``````

To fit an arbitrary curve we must first define it as a function. We can then call `scipy.optimize.curve_fit` which will tweak the arguments (using arguments we provide as the starting parameters) to best fit the data. In this example we will use a single exponential decay function.

``````def monoExp(x, m, t, b):
return m * np.exp(-t * x) + b``````

In biology / electrophysiology biexponential functions are often used to separate fast and slow components of exponential decay which may be caused by different mechanisms and occur at different rates. In this example we will only fit the data to a method with a exponential component (a monoexponential function), but the idea is the same.

``````# perform the fit
p0 = (2000, .1, 50) # start with values near those we expect
params, cv = scipy.optimize.curve_fit(monoExp, xs, ys, p0)
m, t, b = params
sampleRate = 20_000 # Hz
tauSec = (1 / t) / sampleRate

# plot the results
plt.plot(xs, ys, '.', label="data")
plt.plot(xs, monoExp(xs, m, t, b), '--', label="fitted")
plt.title("Fitted Exponential Curve")

# inspect the parameters
print(f"Y = {m} * e^(-{t} * x) + {b}")
print(f"Tau = {tauSec * 1e6} µs")``````

``````Y = 2666.499 * e^(-0.332 * x) + 42.494
Tau = 150.422 µs``````

## Extrapolating the Fitted Curve

We can use the calculated parameters to extend this curve to any position by passing X values of interest into the function we used during the fit.

The value at time 0 is simply `m + b` because the exponential component becomes e^(0) which is 1.

``````xs2 = np.arange(25)
ys2 = monoExp(xs2, m, t, b)

plt.plot(xs, ys, '.', label="data")
plt.plot(xs2, ys2, '--', label="fitted")
plt.title("Extrapolated Exponential Curve")``````

## Constraining the Infinite Decay Value

What if we know our data decays to 0? It's not best to fit to an exponential decay function that lets the `b` component be whatever it wants. Indeed, our fit from earlier calculated the ideal `b` to be `42.494` but what if we know it should be `0`? The solution is to fit using an exponential function where `b` is constrained to 0 (or whatever value you know it to be).

``````def monoExpZeroB(x, m, t):
return m * np.exp(-t * x)

# perform the fit using the function where B is 0
p0 = (2000, .1) # start with values near those we expect
paramsB, cv = scipy.optimize.curve_fit(monoExpZeroB, xs, ys, p0)
mB, tB = paramsB
sampleRate = 20_000 # Hz
tauSec = (1 / tB) / sampleRate

# inspect the results
print(f"Y = {mB} * e^(-{tB} * x)")
print(f"Tau = {tauSec * 1e6} µs")

# compare this curve to the original
ys2B = monoExpZeroB(xs2, mB, tB)
plt.plot(xs, ys, '.', label="data")
plt.plot(xs2, ys2, '--', label="fitted")
plt.plot(xs2, ys2B, '--', label="zero B")``````
``````Y = 1245.580 * e^(-0.210 * x)
Tau = 237.711 µs``````

The curves produced are very different at the extremes (especially when time is 0), even though they appear to both fit the data points nicely. Which curve is more accurate? That depends on your application. A hint can be gained by inspecting the time constants of these two curves.

Parameter Fitted B Fixed B
m 2666.499 1245.580
t 0.332 0.210
Tau 150.422 µs 237.711 µs
b 42.494 0

By inspecting Tau I can gain insight into which method may be better for me to use in my application. I expect Tau to be near 250 µs, leading me to trust the fixed-B method over the fitted B method. Choosing the correct method has great implications on the value of `m` (which is also the value of the curve when time is 0).

# Signal Filtering in Python

Over a decade ago I posted code demonstrating how to filter data in Python, but there have been many improvements since then. My original posts (1, 2, 3, 4) required creating discrete filtering functions, but modern approaches can leverage Numpy and Scipy to do this more easily and efficiently. In this article we will use `scipy.signal.filtfilt` to apply low-pass, high-pass, and band-pass filters to reduce noise in an ECG signal (stored in ecg.wav (created as part of my Sound Card ECG project).

Moving-window filtering methods often result in a filtered signal that lags behind the original data (a phase shift). By filtering the signal twice in opposite directions `filtfilt` cancels-out this phase shift to produce a filtered signal which is nicely aligned with the input data.

``````import scipy.io.wavfile
import scipy.signal
import numpy as np
import matplotlib.pyplot as plt

# read ECG data from the WAV file
times = np.arange(len(data))/sampleRate

# apply a 3-pole lowpass filter at 0.1x Nyquist frequency
b, a = scipy.signal.butter(3, 0.1)
filtered = scipy.signal.filtfilt(b, a, data)``````

``````# plot the original data next to the filtered data

plt.figure(figsize=(10, 4))

plt.subplot(121)
plt.plot(times, data)
plt.title("ECG Signal with Noise")
plt.margins(0, .05)

plt.subplot(122)
plt.plot(times, filtered)
plt.title("Filtered ECG Signal")
plt.margins(0, .05)

plt.tight_layout()
plt.show()``````

## Cutoff Frequency

The second argument passed into the `butter` method customizes the cut-off frequency of the Butterworth filter. This value (Wn) is a number between 0 and 1 representing the fraction of the Nyquist frequency to use for the filter. Note that Nyquist frequency is half of the sample rate. As this fraction increases, the cutoff frequency increases. You can get fancy and express this value as 2 * Hz / sample rate.

``````plt.plot(data, '.-', alpha=.5, label="data")

for cutoff in [.03, .05, .1]:
b, a = scipy.signal.butter(3, cutoff)
filtered = scipy.signal.filtfilt(b, a, data)
label = f"{int(cutoff*100):d}%"
plt.plot(filtered, label=label)

plt.legend()
plt.axis([350, 500, None, None])
plt.title("Effect of Different Cutoff Values")
plt.show()``````

## Improve Edges with Gustafsson’s Method

Something weird happens at the edges. There's not enough data "off the page" to know how to smooth those points, so what should be done?

Padding is the default behavior, where edges are padded with with duplicates of the edge data points and smooth the trace as if those data points existed. The drawback of this is that one stray data point at the edge will greatly affect the shape of your smoothed data.

Gustafsson’s Method may be superior to padding. The advantage of this method is that stray points at the edges do not greatly influence the smoothed curve at the edges. This technique is described in a 1994 paper by Fredrik Gustafsson. "Initial conditions are chosen for the forward and backward passes so that the forward-backward filter gives the same result as the backward-forward filter." Interestingly this paper demonstrates the method by filtering noise out of an EKG recording.

``````# A small portion of data will be inspected for demonstration
segment = data[350:400]

filtered = scipy.signal.filtfilt(b, a, segment)
filteredGust = scipy.signal.filtfilt(b, a, segment, method="gust")

plt.plot(segment, '.-', alpha=.5, label="data")
plt.plot(filteredGust, 'k', label="Gustafsson")
plt.legend()
plt.show()``````

## Band-Pass Filter

Low-pass and high-pass filters can be selected simply by customizing the third argument passed into the filter. The second argument indicates frequency (as fraction of Nyquist frequency, half the sample rate). Passing a list of two values in for the second argument allows for band-pass filtering of a signal.

``````b, a = scipy.signal.butter(3, 0.05, 'lowpass')
filteredLowPass = scipy.signal.filtfilt(b, a, data)

b, a = scipy.signal.butter(3, 0.05, 'highpass')
filteredHighPass = scipy.signal.filtfilt(b, a, data)

b, a = scipy.signal.butter(3, [.01, .05], 'band')
filteredBandPass = scipy.signal.lfilter(b, a, data)``````

## Filter using Convolution

Another way to low-pass a signal is to use convolution. In this method you create a window (typically a bell-shaped curve) and convolve the window with the signal. The wider the window is the smoother the output signal will be. Also, the window must be normalized so its sum is 1 to preserve the amplitude of the input signal.

There are different ways to handle what happens to data points at the edges (see `numpy.convolve` for details), but setting `mode` to `valid` delete these points to produce an output signal slightly smaller than the input signal.

``````# create a normalized Hanning window
windowSize = 40
window = np.hanning(windowSize)
window = window / window.sum()

# filter the data using convolution
filtered = np.convolve(window, data, mode='valid')``````

``````plt.subplot(131)
plt.plot(kernel)
plt.title("Window")

plt.subplot(132)
plt.plot(data)
plt.title("Data")

plt.subplot(133)
plt.plot(filtered)
plt.title("Filtered")``````

Different window functions filter the signal in different ways. Hanning windows are typically preferred because they have a mostly Gaussian shape but touch zero at the edges. For a discussion of the pros and cons of different window functions for spectral analysis using the FFT, see my notes on FftSharp.

# Microcontroller Action Potential Generator

Here I demonstrate how to use a single microcontroller pin to generate action-potential-like waveforms. The output is similar my fully analog action potential generator circuit, but the waveform here is created in an entirely different way. A microcontroller is at the core of this project and determines when to fire action potentials. Taking advantage of the pseudo-random number generator (rand() in AVR-GCC's stdlib.h), I am able to easily produce unevenly-spaced action potentials which more accurately reflect those observed in nature. This circuit has a potentiometer to adjust the action potential frequency (probability) and another to adjust the amount of overshoot (afterhyperpolarization, AHP). I created this project because I wanted to practice designing various types of action potential measurement circuits, so creating an action potential generating circuit was an obvious perquisite.

The core of this circuit is a capacitor which is charged and discharged by toggling a microcontroller pin between high, low, and high-Z states. In the high state (pin configured as output, clamped at 5V) the capacitor charges through a series resistor as the pin sources current. In the low state (pin configured as output, clamped at 0V) the capacitor discharges through a series resistor as the pin sinks current. In the high-Z / high impedance state (pin configured as an input and little current flows through it), the capacitor rests. By spending most of the time in high-Z then rapidly cycling through high/low states, triangular waveforms can be created with rapid rise/fall times. Amplifying this transient and applying a low-pass filter using a single operational amplifier stage of an LM-358 shapes this transient into something which resembles an action potential. Wikipedia has a section describing how to use an op-amp to design an active low-pass filter like the one used here.

The code to generate the digital waveform is very straightforward. I'm using PB4 to charge/discharge the capacitor, so the code which actually fires an action potential is as follows:

``````// rising part = charging the capacitor
DDRB|=(1<<PB4); // make output (low Z)
PORTB|=(1<<PB4); // make high (5v, source current)
_delay_ms(2); // 2ms rise time

// falling part
DDRB|=(1<<PB4); // make output (low Z)
PORTB&=~(1<<PB4); // make low (0V, sink current)
_delay_ms(2); // 2ms fall time
_delay_us(150); // extra fall time for AHP

DDRB&=~(1<<PB4); // make input (high Z)``````

Programming the microcontroller was accomplished after it was soldered into the device using test clips attached to my ICSP (USBtinyISP). I only recently started using test clips, and for one-off projects like this it's so much easier than adding header sockets or even wiring up header pins.

I am very pleased with how well this project turned out! I now have an easy way to make irregularly-spaced action potentials, and have a great starting point for future projects aimed at measuring action potential features using analog circuitry.

### Notes

• Action potential half-width (relating to the speed of the action potential) could be adjusted in software by reducing the time to charge and discharge the capacitor. A user control was not built in to the circuit shown here, however it would be very easy to allow a user to switch between regular and fast-spiking action potential waveforms.
• I am happy that using the 1n4148 diode on the positive input of the op-amp works, but using two 100k resistors (forming a voltage divider floating around 2.5V) at the input and reducing the gain of this stage may have produced a more reliable result.
• Action potential frequency (probability) is currently detected by sensing the analog voltage output by a rail-to-rail potentiometer. However, if you sensed a noisy line (simulating random excitatory and inhibitory synaptic input), you could easily make an integrate-and-fire model neuron which fires in response to excitatory input.
• Discussion related to the nature of this "model neuron" with respect to other models (i.e., Hodgkin–Huxley) are on the previous post.
• Something like this would make an interesting science fair project

# Action Potential Generator Circuit

Few biological cells are as interesting to the electrical engineer as the neuron. Neurons are essentially capacitors (with a dielectric cell membrane separating conductive fluid on each side) with parallel charge pumps, leak currents, and nonlinear voltage-dependent currents. When massively parallelized, these individual functional electrical units yield complex behavior and underlie consciousness. The study of the electrical properties of neurons (neurophysiologically, a subset of electrophysiology) often involves the development and use of sensitive electrical equipment aimed at studying these small potentials produced by neurons and currents which travel through channels embedded in their membranes. It seems neurophysiology has gained an emerging interest from the hacker community, as evidenced by the success of Back Yard Brains, projects like the OpenEEG, and Hack-A-Day's recent feature The Neuron - a Hacker's Perspective.

While contemplating designs for action potential detection and analysis circuitry, I realized that it would be beneficial to be able to generate action-potential-like waveforms on my workbench. The circuit I came up with to do this is a fully analog (technically mixed signal) action potential generator which produces lifelike action potentials.

Cellular Neurophysiology for Electrical Engineers (in 2 sentences): Neuron action potentials (self-propagating voltage-triggered depolarizations) in individual neurons are measured in scientific environments using single cell recording tools such as sharp microelectrodes and patch-clamp pipettes. Neurons typically rest around -70mV and when depolarized (typically by external excitatory input) above a threshold they engage in a self-propagating depolarization until they reach approximately +40mV, at which time a self-propagating repolarization occurs (often over-shooting the initial rest potential by several mV), then the cell slowly returns to the rest voltage so after about 50ms the neuron is prepared to fire another action potential. Impassioned budding electrophysiologists may enjoy further reading _Active Behavior of the Cell Membrane _and Introduction to Computational Neuroscience.

The circuit I describe here produces waveforms which visually mimic action potentials rather than serve to replicate the exact conductances real neurons employ to exhibit their complex behavior. It is worth noting that numerous scientists and engineers have designed more physiological electrical representations of neuronal circuitry using discrete components. In fact, the Hodgkin-Huxley model of the initiation and propagation of action potentials earned Alan Hodgkin and Andrew Huxley the Nobel Prize in Physiology and Medicine in 1936. Some resources on the internet describe how to design lifelike action potential generating circuits by mimicking the endogenous ionic conductances which underlie them, notably Analog and Digital Hardware Neural Models, Active Cell Model, and Neuromorphic Silicon Neuron Circuits. My goal for this project is to create waveforms which resemble action potentials, rather than waveforms which truly model them. I suspect it is highly unlikely I will earn a Nobel Prize for the work presented here.

The analog action potential simulator circuit I came up with creates a continuous series action potentials. This is achieved using a 555 timer (specifically the NE555) in an astable configuration to provide continuous square waves (about 6 Hz at about 50% duty). The rising edge of each square wave is isolated with a diode and used to charge a capacitor. While the charge on the capacitor is above a certain voltage, an NPN transistor (the 2N3904) allows current to flow, amplifying this transient input current. The capacitor discharges predictably (as an RC circuit) through a leak resistor. A large value leak resistor slows the discharge and allows that signal's transistor to flow current for a longer duration. By having two signals (fast and slow) using RC circuits with different resistances (smaller and larger), the transistors are on for different durations (shorter and longer). By making the short pulse positive (using the NPN in common collector configuration) and the longer pulse negative (using the NPN in common emitter configuration), a resistor voltage divider can be designed to scale and combine these signals into an output waveform a few hundred mV in size with a 5V power supply. Pictured below is the output of this circuit realized on a breadboard. The blue trace is the output of the 555 timer.

Between the capacitance of the rectification diode, input capacitance of the transistor, and stray parasitic capacitance from the physical construction of my wires and the rails on my breadboard, there is sufficient capacitance to accumulate charge which can be modified by changing the value of the leak resistor.

This circuit produces similar output when simulated. I'm using LTspice (free) to simulate this circuit. The circuit shown is identical to the one hand-drawn and built on the breadboard, with the exception that an additional 0.1 µF capacitor to ground is used on the output to smooth the signal. On the breadboard this capacitance-based low-pass filtering already exists due to the capacitive nature of the components, wires, and rails.

A few improvements naturally come to mind when considering this completed, functional circuit:

• Action potential frequency: The resistor/capacitor network on the 555 timer determines the rate of square pulses which trigger action potentials. Changing these values will cause a different rate of action potential firing, but I haven't attempted to push it too fast and suspect the result would not be stable is the capacitors are not given time to fully discharge before re-initiating subsequent action potentials.

• Microcontroller-triggered action potentials: Since action potentials are triggered by any 5V rising edge signal, it is trivially easy to create action potentials from microcontrollers! You could create some very complex firing patterns, or even "reactive" firing patterns which respond to inputs.

For example, add a TSL2561 I2C digital light sensor and you can have a light-to-frequency action potential generator!

• Adjusting size and shape of action potentials: Since the waveform is the combination of two waveforms, you can really only adjust the duration (width) or amplitude (height) of each individual waveform, as well as the relative proportion of each used in creating the summation. Widths are adjusted by changing the leak resistor on the base of each transistor, or by adding additional capacitance. Amplitude and the ratio of each signal may be adjusted by changing the ratio of resistors on the output resistor divider.

• Producing -70 mV (physiological) output: The current output is electirically decoupled (through a series capacitor) so it can float at whatever voltage you bias it to. Therefore, it is easy to "pull" in either direction. Adding a 10k potentiometer to bias the output is an easy way to let you set the voltage. A second potentiometer gating the magnitude of the output signal will let you adjust the height of the output waveform as desired.

• The 555 could be replaced by an inverted ramp (sawtooth): An inverted ramp / sawtooth pattern which produces rapid 5V rising edges would drive this circuit equally well. A fully analog ramp generator circuit can be realized with 3 transistors: essentially a constant current capacitor charger with a threshold-detecting PNP/NPN discharge component.

• This action potential is not all-or-nothing: In real life, small excitatory inputs which fail to reach the action potential threshold do not produce an action potential voltage waveform. This circuit uses 5V rising edges to produce action potential waveforms. However, feeding a 1V rising edge would produce an action potential 1/5 the size. This is not a physiological effect. However, it is unlikely (if not impossible) for many digital signal sources (i.e., common microcontrollers) to output anything other than sharp rising edge square waves of fixed voltages, so this is not a concern for my application.

• Random action potentials: When pondering how to create randomly timed action potentials, the issue of how to generate random numbers arises. This is surprisingly difficult, especially in embedded devices. If a microcontroller is already being used, consider Make's write-up on the subject, and I think personally I would go with a transistor-based avalanche nosie generator to create the randomness.

• A major limitation is that irregularly spaced action potentials have slightly different amplitudes.I found this out the next day when I created a hardware random number generator (yes, that happened) to cause it to fire regularly, missing approximately half of the action potentials. When this happens, breaks in time result in a larger subsequent action potential. There are several ways to get around this, but it's worth noting that the circuit shown here is best operated around 6 Hz with only continuous regularly-spaced action potentials.

In the video I also demonstrate how to record the output of this circuit using a high-speed (44.1 kHz) 16-bit analog-to-digital converter you already have (the microphone input of your sound card). I won't go into all the details here, but below is the code to read data from a WAV file and plot it as if it were a real neuron. The graph below is an actual recording of the circuit described here using the microphone jack of my sound card.

``````import numpy as np
import matplotlib.pyplot as plt
Ys = np.memmap("recording.wav", dtype='h', mode='r')[1000:40000]
Ys = np.array(Ys)/max(Ys)*150-70
Xs = np.arange(len(Ys))/44100*1000
plt.figure(figsize=(6,3))
plt.grid(alpha=.5,ls=':')
plt.plot(Xs,Ys)
plt.margins(0,.1)
plt.title("Action Potential Circuit Output")
plt.ylabel("potential (mV)")
plt.xlabel("time (ms)")
plt.tight_layout()
plt.savefig("graph.png")
#plt.show()
``````

Let's make some noise! Just to see what it would look like, I created a circuit to generate slowly drifting random noise. I found this was a non-trivial task to achieve in hardware. Most noise generation circuits create random signals on the RF scale (white noise) which when low-pass filtered rapidly approach zero. I wanted something which would slowly drift up and down on a time scale of seconds. I achieved this by creating 4-bit pseudo-random numbers with a shift register (74HC595) clocked at a relatively slow speed (about 200 Hz) having essentially random values on its input. I used a 74HC14 inverting buffer (with Schmidt trigger inputs) to create the low frequency clock signal (about 200 Hz) and an extremely fast and intentionally unstable square wave (about 30 MHz) which was sampled by the shift register to generate the "random" data. The schematic illustrates these points, but note that I accidentally labeled the 74HC14 as a 74HC240. While also an inverting buffer the 74HC240 will not serve as a good RC oscillator buffer because it does not have Schmidt trigger inputs.

An inverting buffer created a fast and a slow clock to produce 4-bit pseudo-random numbers:

reminder how an inverting buffer can act as an oscillator:

the full circuit realized on the breadboard:

output of the 4-bit pseudo-random number generator:

4-bit output smoothed through a single-stage RC filter:

noise combined with action potential waveforms:

The addition of noise was a success, from an electrical and technical sense. It isn't particularly physiological. Neurons would fire differently based on their resting membrane potential, and the peaks of action potential should all be about the same height regardless of the resting potential. However if one were performing an electrical recording through a patch-clamp pipette in perforated patch configuration (with high resistance between the electrode and the internal of the cell), a sharp microelectrode (with high resistance due to the small size of the tip opening), or were using electrical equipment or physical equipment with amplifier limitations, one could imagine that capacitance in the recording system would overcome the rapid swings in cellular potential and result in "noisy" recordings similar to those pictured above. They're not physiological, but perhaps they're a good electrical model of what it's like trying to measure a physiological voltage in a messy and difficult to control experimental environment.

This project was an interesting exercise in analog land, and is completed sufficiently to allow me to move toward my initial goal: creating advanced action potential detection and measurement circuitry. There are many tweaks which may improve this circuit, but as it is good enough for my needs I am happy to leave it right where it is. If you decide to build a similar circuit (or a vastly different circuit to serve a similar purpose), send me an email! I'd love to see what you came up with.

I enhanced this project by creating a microcontroller controlled action potential generator. That article is here: https://www.swharden.com/wp/2017-08-20-microcontroller-action-potential-generator/

Articles typically receive this designation when the technology they describe is no longer relevant, code provided is later deemed to be of poor quality, or the topics discussed are better presented in future articles. Articles like this are retained for the sake of preservation, but their content should be critically assessed.

# VHF Frequency Counter with PC Interface

Projects I build often involve frequency synthesis, and one of the most useful tools to have around is a good frequency counter. I love the idea of being able to access / log / analyze frequency readings on my computer. Commercial frequency counters can be large, expensive, and their calibration is a chicken-and-egg problem (you need a calibrated frequency counter to calibrate a frequency reference you use to calibrate a frequency counter!). For about the cost of a latte I made a surprisingly good frequency frequency counter (which directly counts >100 MHz without dividing-down the input signal) by blending a SN74LV8154 dual 16-bit counter (which can double as a 32-bit counter, \$1.04 on mouser) and an ATMega328 microcontroller (\$3.37 on Mouser).

Although these two chips are all you need to count something, the accuracy of your counts depend on your gate. If you can generate a signal of 1 pulse per second (1PPS), you can count anything, but your accuracy depends on the accuracy of your 1PPS signal. To eliminate the need for calibration (and to provide the 1PPS signal with the accuracy of an atomic clock) I'm utilizing the 1PPS signal originating from a GPS unit which I already had distributed throughout my shack (using a 74HC240 IC as a line driver). If you don't have a GPS unit, consider getting one! I'm using a NEO-6M module (\$17.66 on Amazon) to generate the 1PPS gate, and if you include its cost we're up to \$22.07. Also, all of the code for this project (schematics, C that runs on the microcontroller, and a Python to interact with the serial port) is shared on GitHub! You may be wondering, "why do GPS units have incredibly accurate 1PPS signals?" It's a good question, but a subject for another day. For now, trust me when I say they're fantastically accurate (but slightly less precise due to jitter) if you're interested in learning more read up on GPS timing.

This is the general idea behind how this frequency counter works. It's so simple! It's entirely digital, and needs very few passive components. sn74lv8154 is configured in 32-bit mode (by chaining together its two 16-bit counters, see the datasheet for details) and acts as the front-end directly taking in the measured frequency. This chip is "rare" in the sense I find very few internet projects using it, and they're not available on ebay. However they're cheap and plentiful on mouser, so I highly encourage others to look into using it! The datasheet isn’t very clear about its maximum frequency, but in my own tests I was able to measure in excess of 100 MHz from a breadboarded circuit! This utilized two cascaded ICS501 PLL frequency multiplier ICs to multiply a signal I had available (the 11.0592 MHz crystal the MCU was running from) by ten, yielding 110 MHz, which it was able to measure (screenshot is down on the page).

The 1PPS gate signal is generated from an inexpensive GPS module available on Amazon. I've hinted at the construction of this device before and made a post about how to send output signals like the 1PPS signal generated here throughout your shack via coax using a line driver, so I won't re-hash all of those details here. I will say that this module has only VCC, GND, and TX/RX pins, so to get access to the 1PPS signal you have to desolder the SMT LED and solder a wire to its pad. It requires a bit of finesse. If you look closely, you can see it in this picture (purple wire).

I first built this device on a breadboard, and despite the rats nest of wires it worked great! Look closely and you can see the ICS501 frequency multiplier ICs I wrote about before. In this case it's measuring the 10x multiplied crystal frequency clocking the MCU (11 MHz -> 110 MHz) and reporting these readings every 1 second to the computer via a serial interface.

Frequency measurements of the VHF signal are reported once per second. Measurements are transmitted through a USB serial adapter, and captured by a Python script. Note that I'm calling this signal VHF because it's >30 MHz. I am unsure if this device will work up to 300 MHz (the border between VHF and UHF), but I look forward to testing that out! Each line contains two numbers: the actual count of the counter (which is configured to simply count continuously and overflow at 2^32=4,294,967,296), and the gated count (calculated by the microcontroller) which is the actual frequency in Hz.

This screenshot shows that my ~11.05 MHz crystal is actually running at 11,061,669.4 Hz. See how I capture the 0.4 Hz unit at the end? That level of precision is the advantage of using this VHF-capable counter in conjunction with a 10x frequency multiplier!

Once I confirmed everything was working, I built this device in a nice enclosure. I definitely splurge every few months and buy extruded split body aluminum enclosures in bulk (ebay), but they're great to have on hand because they make projects look so nice. I added some rubber feet (cabinet bumpers from Walmart), drilled holes for all the connectors with a continuous step drill bit, made a square hole for the serial port using a nibbler, and the rest is pretty self-evident. Labels are made with a DYMO LetraTag (Target) and clear labels (Target, Amazon) using a style inspired by PA2OHH. I tend to build one-off projects like this dead-bug / Manhattan style.

I super-glued a female header to the aluminum frame to make in-circuit serial programming (ICSP) easy. I can't believe I never thought to do this before! Programming (and reprogramming) was so convenient. I'm going to start doing this with every enclosed project I build from now on. FYI I'm using a USBTiny ISP (\$10.99, Amazon) to do the programming (no longer the BusPirate, it's too slow) like I describe here for 64-bit Windows 7 (although I'm now using Windows 10 and it works the same).

The front of the device has LEDs indicating power, serial transmission, and gating. Without a 1PPS gate, the device is set to send a count (of 0) every 5 seconds. In this case, the TX light will illuminate. If a gate is detected, the TX and GATE LEDs will illuminate simultaneously. In reality I just drilled 3 holes when I really needed two, so I had to make-up a function for the third LED (d'oh!)

The back of the device has serial output, frequency input, gate input, and power. Inside is a LM7805 voltage regulator, and careful attention was paid to decoupling and keeping ripple out of the power supply (mostly so our gate input wouldn't be affected). I'm starting to get in the habit of labeling all serial output ports with the level (TTL vs CMOS, which makes a HUGE difference as MAX232 level converter may be needed, or a USB serial adapter which is capable of reading TTL voltages), as well as the baud rate (119200), byte size (8), parity (N), and stop bit (1). _I just realized there's a typo! The label should read 8N1. I don't feel like fixing it, so I'll use a marker to turn the 2 into an 8. _I guess I'm only human after all.

I should have tried connecting all these things before I drilled the holes. I got so lucky that everything fit, with about 2mm to spare between those BNC jacks. Phew!

This is an easy test frequency source. I have a dozen canned oscillators of various frequencies. This is actually actually a voltage controlled oscillator (VCO) with adjustment pin (not connected), and it won't be exactly 50 MHz without adjustment. It's close enough to test with though! As this is >30 MHz, we can call the signal VHF.

You can see on the screen it's having no trouble reading the ~50 MHz frequency. You'll notice I'm using RealTerm (with a good write-up on sparkfun) which is my go-to terminal program instead of HyperTerminal (which really needs to go away forever). In reviewing this photo, I'm appreciating how much unpopulated room I have on the main board. I'm half tempted to build-in a frequency multiplier circuit, and place it under control of the microcontroller such that if an input frequency from 1-20MHz is received, it will engage the 10x multiplier. That's a mod for another day though! Actually, since those chips are SMT, if I really wanted to do this I would make this whole thing a really small SMT PCB and greatly simplify construction. That sounds like a project for another day though...None

Before closing it up I added some extra ripple protection on the primary counter chip. There's a 560 uH series inductor with the power supply, followed by a 100 nF capacitor parallel with ground. I also added ferrite beads to the MCU power line and gate input line. I appreciate how the beads are unsecured and that this is a potential weakness in the construction of this device (they're heavy, so consider what would happen if you shook this enclosure). However, anything that would yank-away cables in the event of shaking the device would probably also break half the other stuff in this thing, so I think it's on par with the less-than-rugged construction used for all the other components in this device. It will live a peaceful life on my shelf. I am not concerned.

This is the final device counting frequency and continuously outputting the result to my computer. In the background you can see the 12V power supply (yellow) indicating it is drawing only 20 mA, and also the GPS unit is in a separate enclosure on the bottom right. Click here to peek inside the GPS 1PPS enclosure.

I'm already loving this new frequency counter! It's small, light, and nicely enclosed (meaning it's safe from me screwing with it too much!). I think this will prove to be a valuable piece of test equipment in my shack for years to come. I hope this build log encourages other people to consider building their own equipment. I learned a lot from this build, saved a lot of money not buying something commercial, had a great time making this device, and I have a beautiful piece of custom test equipment that does exactly what I want.

## Source Code

Microcontroller code (AVR-GCC), schematics, and a Python script to interface with the serial port are all available on this project's GitHub page

## Afterthought: Using without GPS

One of the great advantages of this project is that it uses GPS for an extremely accurate 1 PPS signal, but what options exist to adapt this project to not rely on GPS? The GPS unit is expensive (though still <\$20) and GPS lock is not always feasible (underground, in a Faraday cage, etc). Barring fancy things like dividing-down rubidium frequency standards or oven controlled oscillators, consider having your microcontroller handle the gating using either interrupts and timers precisely configured to count seconds. Since this project uses a serial port with a 11.0592 MHz crystal, your 1PPS stability will depend on the stability of your oscillator (which is pretty good!). Perhaps more elegantly you could use a 32.768 kHz crystal oscillator to create a 1 PPS signal. This frequency can be divided by 2 over and over to yield 1 Hz perfectly. This is what most modern wristwatches do. Many AVRs have a separate oscillator which can accomodate a 32 kHz crystal and throw interrupts every 1 second without messing with the system clock. Alternatively, the 74GC4060 (a 14 stage ripple counter) can divide 32k into 1 Hz and even can be arranged as an oscillator (check the datasheet). It would be possible to have both options enabled (local clock and GPS) and only engage the local clock if the GPS signal is absent. If anyone likes the idea of this simple VHF frequency counter with PC interface but doesn't want to bother with the GPS, there are plenty of options to have something almost as accurate. That really would cut the cost of the final device down too, keeping it under the \$5 mark.

## Update: Integrating Counter Serial Output with GPS Serial Output

The NEO-M8 GPS module is capable of outputting serial data at 9600 baud and continuously dumps NEMA formatted GPS data. While this isn't really useful for location information (whose frequency counter requires knowing latitude and longitude?) it's great for tracking things like signal strength, fix quality, and number of satellites. After using this system to automatically log frequency of my frequency reference, I realized that sometimes I'd get 1-2 hours of really odd data (off by kHz, not just a few Hz). Power cycling the GPS receiver fixes the problem, so my guess it that it's a satellite issue. If I combine the GPS RX and counter in 1 box, I could detect this automatically and have the microcontroller power cycle the GPS receiver (or at the least illuminate a red error LED). I don't feel like running 2 USB serial adapters continuously. I don't feel like programming my AVR to listen to the output from the GPS device (although that's probably the correct way to do things). Instead I had a simpler idea that worked really well, allowing me to simultaneously log serial data from my GPS unit and microcontroller (frequency counter) using 1 USB serial adapter.

The first thing I did was open up the frequency counter and reconnect my microcontroller programmer. This is exactly what I promised myself I wouldn't do, and why I have a nice enclosure in the first place! Scott, stop fidgeting with things! The last time I screwed this enclosure together I considered adding super glue to the screw threads to make sure I didn't open it again. I'll keep my modifications brief! For now, this is a test of a concept. When it's done, I'll revert the circuitry to how it was and close it up again. I'll take what I learn and build it into future projects.

I peeked at the serial signals of both the frequency counter (yellow) and the GPS unit output (blue). To my delight, there was enough dead space that I thought I could stick both in the same signal. After a code modification, I was able to tighten it up a lot, so the frequency counter never conflicts with the GPS unit by sending data at the same time.

I had to slow the baud rate to 9600, but I programmed it to send fewer characters. This leaves an easy ~50ms padding between my frequency counter signal and the GPS signal. Time to mix the two! This takes a little thought, as I can't just connect the two wires together. Serial protocol means the lines are usually high, and only pulled down when data is being sent. I had to implement an active circuit.

Using a few components, I built an AND gate to combine signals from the two serial lines. For some reason it took some thought before I realized an AND gate was what I needed here, but it makes sense. The output is high (meaning no serial signal) only when both inputs are high (no serial signals on the input). When either signal drops low, the output drops low. This is perfect. My first thought was that I'd need a NOR gate, but an inverted AND gate is a NOR gate.

Here's my quick and dirty implementation. A reminder again is that this will be removed after this test. For now, it's good enough.

After connecting the GPS serial output and frequency counter serial output to the AND gate (which outputs to the computer), I instantly got the result I wanted!

RealTerm shows that both inputs are being received. It's a mess though. If you want to know what everything is, read up on NEMA formatted GPS data.

I whipped-up a python program to parse, display, and log key information. This display updates every 1 second. The bottom line is what is appended to the log file on ever read. It's clunky, but again this is just for testing and debugging. I am eager to let this run for as long as I can (days?) so I can track how changes in satellite signal / number / fix quality influence measured frequency.