Part selection can be quite daunting for someone learning electronics. I’ve experienced first-hand that most of the time, parts are selected for you in class. There is sort of an art and mathematical process to figuring out what you need to start with. As I mentioned in my first TechForum post, the datasheet for the NE556N certainly gives maximum ratings and important equations for timing purposes. It does not discuss part selection.
About Datasheet Equations
Since my application is astable, the necessary information can be found starting on page 8 through 9 of the datasheet. For first time learners, many are taught that equations are something to solve. That isn’t too far from the truth, but this sort of lacks context. Here is something I’ve observed during this process that may not be immediately apparent:
The datasheet equations are already presented as design models. It’s not for derivation, it’s used to decide which variables to choose first.
The method in how we accomplish this is the “difficult part.” First of all, we have to determine which equation is “most relevant to us.” Since I selected a frequency range of 1 to 60Hz, we will want to look at the “T” equation (or period). The relationship between period and frequency is that 1/F = T or 1/T = F. A period is defined as the time it takes for a waveform to complete one full cycle. For a square wave, one example is the first rising edge to the next rising edge.
Finding T (Period)
Great, so we can define what T is. What end do we start with, 1Hz or 60Hz? The short answer is start with the faster frequency based on my experimentation. The simple explanation is how capacitors charge in terms of tau ( or the time constant):
τ=RC
Since the capacitor is going to stay constant, increasing resistance naturally increases the value of Tau. It takes five times tau to have a capacitor reach about 99% charge. Since tau is in seconds, you can’t have this decrease in value (getting faster) without R already starting large and getting smaller. This is why I found out that 1/60 is a good starting point for T.
Finding…the rest
That still means we are dealing with Ct, Ra, and Rb. That is three unknowns and no more equations to work with. This is where some might stop because it’s “unsolvable.” Mathematically, that is correct. This is not how equations are practically used in circuit development though. This is where knowing a little bit of algebra helps and knowing where to go from here.
What Capacitance and Resistance to Select?
There are a few different ways to approach this. I definitely wouldn’t pick haphazardly as many beginners do. Google can help, but the advice varies. Some might just “pick a large capacitance” if you need it to go slow. This is partially true and might actually damage your 555 timer if you pick something too large! It depends what your starting frequency is, but for 60 Hz, do not exceed 57.105µF! I’d say to pick with something much lower than that. For context, I arbitrarily chose 50µF because I just thought it was a fine starting point. The value I mentioned comes from the 555’s internal discharge current limitations. If you’d like to see how I came to this, check out this related, optional TechForum post.
For the resistance values, first I used algebra to solve for Ra and Rb:
This way, you can use something some teachers refer to as the “plug and chug” method. We know what T is and I selected a 50µF capacitor. All that leaves is Ra or Rb. This solving method is quite simple, pick a value for Ra or Rb and solve for the only variable left. You can put these as expressions in Excel or whatever spreadsheet application you have access to. You can set up constants in cells for T, CT, and pick values for Ra or Rb, then write the equation for the last variable in the same terms as the solved equation. Please note that sometimes you may get answers below zero, you can adjust Ra or Rb until the other value is positive or you can write an inequality equation to figure out what the limits are. Here is a snapshot of the table I came up with:
I adjusted my Ra value until I got a positive number for Rb. This gives me a minimum parameter and a maximum parameter for Rb by changing the time period by adding 20ms to the period and keeping 250 for Ra. The maximum resistance for Rb I chose was 10k and the minimum of 110 is close enough to 81.
Last Note About Component Selection
Now that you know more about how I selected the base values for my first prototype, I wanted to make a final remark about the ratings of the components. I didn’t have much to go on for the amount of current the resistors would see at that moment and didn’t know the “exact” voltage ratings. The voltage source I chose is a simple AC to DC supply capable of delivering up to 1.2A. I knew it wasn’t feasible that my resistors would ever draw more than 1A, but wasn’t entirely confident on what the timing resistors would draw before the experimentation (I wasn’t entirely sure how the astable mode worked yet).
I do know what the LEDs would draw, the IC can only supply up to 200mA maximum. I selected resistors for my LEDs first (you can learn more about that here). Since I knew what my LEDs would draw, it seemed like a safe assumption that it it would be similar to my timing resistors. I utilized my maximum Vcc voltage of 5V as something to start with. As a conservative worst-case estimate, I assumed the full 5V over the lowest resistance of 110 Ω’s. Take that current and multiply it by the voltage. You will get 0.227W. At the very minimum, 1/4W resistors seemed fine based on that assumption alone. You can technically select higher wattages (one of my parts is 1/2W), but you will have larger parts, usually.
For the capacitor, we are only dealing with voltage ratings. 5V is the absolute max here, so anything with a 5V or higher rating is fine. Many often think you will lose performance if you go way over, but for this application a capacitor rating significantly over 5V did not noticeably affect circuit operation.