If you have been wondering on how to select resistor values for your circuit, or you are amazed at how circuits were designed using the appropriate values, this is the right article for you. Before going into proper explanation and analysis, let us take a portion of the book “ The Art of Electronics”.
A large resistor in series (parallel) with a small resistor has the resistance of the larger (smaller) one, roughly. So you can “trim” the value of a resistor up or down by connecting a second resistor in series or parallel: to trim up, choose an available resistor value below the target value, then add a (much smaller) series resistor to make up the difference; to trim down, choose an available resistor value above the target value, then connect a (much larger) resistor in parallel. For the latter you can approximate with proportions – to lower the value of a resistor by 1%, say, put a resistor 100 times as large in parallel.
Meaning
“A large resistor in series with a small resistor has the resistance of the larger one, roughly. So you can “trim” the value of a resistor by connecting a second resistor in series: to trim up, choose an available resistor value below the target value, then add a (much smaller) series resistor to make up the difference."
The total of the two resistor values will equal the equivalent resistance of two resistors connected in series for the series situation. You might connect a 100 Ohm and a 10 Ohm resistor in series to create a 110 Ohm resistor.
"A large resistor in parallel with a small resistor has the resistance of the smaller one, roughly. So you can “trim” the value of a resistor down by connecting a second resistor in parallel: to trim down, choose an available resistor value above the target value, then connect a (much larger) resistor in parallel."
Keep in mind that in the parallel scenario, the equivalent resistance of two resistors will be lower than the resistance of the resistor with the lower value.
For resistors in parallel the total value will be less than the lowest value resistor. The equation for parallel resistors is: 11/R3+1/R4. Take the reciprocal of each resistor and add them, then take the reciprocal of that total. This answer is 990.099 ohms, a drop of 1% for R3.
This method is useful because it enables distraction-free, fast mental circuit analysis. For concept generation, we aim to promote mental designing, or at the very least "back of the envelope" creation.
You should make an effort to prevent developing this habit for the following two reasons:
- The components themselves are of limited accuracy (resistors normally have tolerances of 5% or 1%; for capacitors, it's often 10% or 5%; and the parameters describing transistors, for example, are sometimes only known to a factor of 2);
- The final circuit's insensitivity to specific component values is an indication of a successful circuit design (there are exceptions, of course). If you develop the practice of making approximations in your brain rather than seeing meaningless numbers appear on a calculator display, you'll also pick up circuit intuition more rapidly. We firmly think that using equations and formulae early in your electronic circuit
education is a fine way to prevent you from understanding what’s really going on.