High- and low-pass RC filters

Having generated a just-about-square wave, I’m fiddling with high-pass and low-pass RC filters (still inspired by Afrotechmods).

I’m still using the 50% duty cycle circuit from the NE555N datasheet, except that R1 is 53K and C1 is 100nF.

I’ve taken that output into a low pass filter: the signal comes through a 10K resistor into the scope, and there’s a 10nF capacitor going to ground.

As expected, with a 139.7Hz input signal, the attack and decay are slowed down a little bit:

139Hz, R1=10K, C1=10nF
138Hz, R1=10K, C1=10nF

Increasing the input signal increases the effect:

138KHz, R1=10K, C1=10nF
138KHz, R1=10K, C1=10nF

Increasing the input signal further to 26.1Khz gives a nice saw triangle wave:

26.1KHz, R1=10K, C1=10nF
26.1KHz, R1=10K, C1=10nF

And increasing it ridiculously produces a DC signal:

261Khz, R1=10K, C1=10nF

I’d like to have made a better saw triangle wave but I don’t have the right value of capacitor for the 555 circuit. However, increasing C1 to 231nF (7x33nF) and setting the input signal back to 139Hz produces a lovely one:

139Hz, R1=10K, C1=231nF
139Hz, R1=10K, C1=231nF

And a very similar wave is produced by setting C1 back to 10nF and increasing R1 to 220K:

139Hz, R1=220K, C1=10nF
139Hz, R1=220K, C1=10nF

This is explained by something called “maths“, but I’m happy enough to see that changing either one works. Afrotechmods suggested selecting the value of R1 to suit the load on the output signal, and changing C1 to get the appropriate wave. Which seems sensible.

Switching the positions of R1 and C1 gives a high pass filter, and as expected, produces the following wave:

140Hz, C1=10nF, R1=220K
140Hz, C1=10nF, R1=220K

In the process of making a silly mistake, I also found that leaving R1 out made the wave much tidier, completely getting rid of the ramping down and up that I couldn’t get eliminate in the 555 circuit! Neat:

No ramping up and down
No ramping up and down

Though, as you would expect from a high pass filter, the peaks and troughs are no longer quite flat. I’m not sure how to expect a high pass filter to behave without R1, so I don’t really know if this is meaningful or useful.

Anyway, decreasing the input signal to 78Hz produces a more pronounced change:

78Hz, C1=10nF, R1=220K
78Hz, C1=10nF, R1=220K

As does decreasing C1 to 1.4nF (3x470pF):

140Hz, C1=1.4nF, R1=220K
140Hz, C1=1.4nF, R1=220K

Decreasing C1 to 1pF gets us back to DC:

140Hz, C1=1pF, R1=220K
140Hz, C1=1pF, R1=220K

As does decreasing R1 to 10R:

140Hz, C1=10nF, R1=10R
140Hz, C1=10nF, R1=10R

However, I couldn’t quite get it back to DC by passing in a lower frequency wave. I made the filter a bit more aggressive by changing R1 to 100K, and passed in 12.5Hz. But no matter how low the frequency, there are always upwards and downwards spikes when the input signal changes from high to low, or vice versa:

12.5Hz, C1=10nF, R1=100K
12.5Hz, C1=10nF, R1=100K

I think I’ll leave that mystery for another day.

Generating a square wave from a 555 timer

Inspired by Afrotechmods, I thought I might try experimenting with RC filters and wave generators. I bought a second probe for my scope so I can see the input and output signals at the same time (neat).

Since I don’t have a signal generator, I thought a good start might be to try making a 555-based circuit that generates a square wave to pass into some filters to see what happens. I did wonder about doing this with an Arduino, but that seems like cheating. And it would be good to get into the habit of doing things in hardware when I can, instead of going straight to a microprocessor.

I’ve also wondered before about producing a 50% duty cycle from a 555, which isn’t something I’ve done — an astable always seems to be more one way than the other, and I’m not sure why. From Wikipedia, I learned that the duty cycle is described as a percentage, where the percentage is the time the signal is high. It can therefore be calculated as:

D = a / P

Where D is the duty cycle, a is the time the signal is active, and P is the period of the wave.

To start with I built the 50% duty cycle circuit from the NE555N datasheet. I don’t have any 51K resistors (which sounds like an odd value) so I used a 47K. Perhaps predictably, the resulting wave was not 50%:

1.228KHz
R1 = 47K, C1 = 10nF, f = 1.228KHz, a = 0.3ms, p = 0.82ms, d = 0.366

Experimenting with the value of C1 produced the results I would expect. With 4.7nF:

1.698KHz
R1 = 47K, C1 = 4.7nF, f = 1.698KHz, a = 0.22ms, p = 0.59ms, d = 0.373

With 4.7 and 10nF in parallel:

0.708KHz
R1 = 47K, C1 = 14.7nF, f = 0.708KHz, a = 0.51, p = 1.39ms, d = 0.367

With 100nF:

109.3Hz
R1 = 47K, C1 = 100nF, f = 119.3Hz, a = 3.2ms, p = 8.5ms, d = 0.376

As expected, the frequency decreases as the value of C1 increases, and the duty cycle stays constant (ish). Less expectedly, the wave is not particularly square. Here is the 50KHz calibration signal from the scope for comparison:

Scope 50KHz
Scope 50KHz

In any case, one thing at a time. The 50% duty cycle might be caused by not following the instructions from the datasheet, so I strung together a 47K and 4 1K resistors to get to the magic number. With C1 at 10nF:

R1=51K
R1 = 51K, C1 = 10nF, f = 1.439KHz, a = 0.32ms, p = 0.7ms, 0.457

This is much closer to 50%, but also rather less square. Guess: the higher resistance is causing the cap to charge more slowly, leading to that slower ramp-up. Let’s try a 100K and see how that looks:

R1=100K
R1 = 100K, C1 = 10nF, f = 1.202KHz, a = 0.64ms, p = 0.66ms, d = 0.969

Guess not. The edges are now more similar to the ones with lower values for R1. *confused*. Looking back over the earlier pictures, I think that ramp-up/down actually gets a bit worse as C1 increases. Which does make sense if C1 is taking longer to charge. Changing C1 to 100nF does back this up a bit:

C1=100nF
R1 = 100K, C1 = 100nF, f = 117.4Hz, a = 6.8ms, p = 7ms, d = 0.971

So I guess it’s some mixture of R1 and C1 that I don’t understand. Gratifyingly, though, those last two pictures show clearly that altering C1 alters the frequency without changing the duty cycle (much), and it looks like that that relationship is linear: multiplying C1 by 10 gave a value of p 10 times greater.

Anyway. I set kept C1 at 100nF, put R1 back to 51K and added two more 1K resistors, bringing the total up to 53K, and that gave me exactly a 50% cycle:

R1=53K
R1 = 53K, C1 = 100nF, f = 1145.5Hz, a = 3.6ms, p = 7.2ms, d = 0.5

Good enough, I think, despite the not-quite-squareness.

I wondered then if the values in the datasheet are correct (which seems likely) and if it’s just the low tolerance on these resistors that’s accounting for the difference. So I measured the actual values of R1 and R2 which were 52.3K and 22.24K respectively. I guess it’s not those then. I swapped out the 555 for a different one in case that was damaged or the tolerances there could make a difference. Nope. The value of C1 doesn’t affect the duty cycle very much, so it’s probably not that. And I can’t measure that. So it’ll have to be a mystery.

Next: adding low- and high-pass RC filters.