# RC Time Constants (Part 2) - Circuit Waveforms

#### Inductors, Capacitors, Transformers

### Circuit Waveforms

This is the final section of 7-4, and we'll be looking at circuit waveforms. Charging and discharging of a capacitor in an RC circuit requires some definite amount of time. The diagram at the right illustrates the response of an RC circuit to three different frequency pulses. Here, we have a series RC circuit, notice the applied voltage is going to be a rectangular-shaped waveform. Here, we see three different possible wave shapes.

Now what we're doing is we're looking at here we have a short time constant where each pulse of the rectangular wave is going to be 10 time constants in length, then we have a moderate time constant where the length of one-half of the rectangular wave is one time constant, and then here where we have only one-tenth of a time constant. This would be called a long time constant.

### Short Time Constant

Let's look at each of these individually. Here, we have a short time constant. In this case, 10-time constants are allowed. The cap has time for a complete discharge. There's a circuit called differentiator if the output is taken across the resistor. What we have here, here we have the applied voltage and this is going to be a very short time constant. Notice, during the time of half this square wave we have 10-time constants. That's going to allow plenty of time for the cap to charge and discharge. Now what you'll note here is that if we measure the voltage across the capacitor and keep in mind here we have an input coming in and this input from this point to this point is going to be 10-time constants. That's going to be plenty of time to charge this capacitor fully. You'll also note this is a voltage across the resistor. During this time, this cap is going to charge quite quickly, and then the voltage across the resistor will effectively be zero. You'll notice here across the resistor there is a spike as the pulse initially is placed in the circuit. We see that pulse and then it deteriorates down to virtually nothing because the all the voltage dropped across the cap.

Then, during this time here, the voltage is removed. This spike right here is what we see as the cap is discharging and we see a short spike across the resistor and the cap deteriorates down to zero because there's a long time for it to discharge. Then, an incoming voltage comes in again and we have the repeat of what we just looked at. The output if taken across the resistor we would simply see the short duration spike and this is a circuit that is referred to as a differentiator.

### Moderate Time Constant

Then, here we have a circuit we're going to call this a moderate time constant. In this case, the time of one pulse would be one time constant. A longer time constant does not allow cap time to fully charge, nor does it have time to fully discharge. In this case, here we have our applied rectangular wave shape and you'll notice the voltage across the resistor it starts out at the applied voltage and then it deteriorates just a little bit because the capacitor here is beginning to charge but it does not have time to fully charge, so we will always see some voltage across this resistor. Then, when we go down to zero volts on our applied voltage suddenly, the cap is discharging and we see this voltage across the resistor and the cap does not have time to fully discharge because there's one time constant, one time constant it will not fully discharge, so across the cap we see this type of a wave shape. This is the result of the cap never fully charging and never fully discharging. This would be the resultant wave that we would see across the resistor.

### Long Time Constant

Then, this is a long time constant. Now, in this case, the time of the rectangular wave there's only one-tenth of a time constant, so the cap is going to have a very limited amount of time to charge or discharge. The cap has little time to increase or decrease. If the output is taken across the resistor it is called an RC coupling circuit. If the output is taken across the cap it is called an integrator. We will talk a little more about coupling and integrators later in this text.

Let's take a quick look at this waveform. You'll notice here we have the applied rectangular wave. The voltage across the resistor, you see there's a peak here and then it slightly levels out. What this slight change here is the result of the capacitor attempting to charge a little bit but never having time to fully charge or fully discharge so the voltage across the cap is not a flat line, but it increases a little and then it decreases a little because it doesn't have time to either charge or discharge. The voltage across the resistor looks somewhat like the input, but it deteriorates just a little bit because of that slight charge on the cap.

### Applications

There are many applications for RC and RL circuits in electronics and computers. Power supply circuits, they're used to filter out the 60 Hz oscillations on DC. Typically, if you had, for example, if you had a rectifier and remember we had AC coming in and we have these pulses coming out, and commonly there would be a capacitor placed something like this and the cap would charge and it would begin to filter out these ripples and you'd have a more stable DC, though they're widely used as filters for power supplies.

They can also be used as passive filter circuits. They can be used to passively select or reject frequencies for low pass, high pass, band pass and band reject, and we will look at all these filtering types when we get into the opt amp section of your text. They can also be used as time delay circuits. The time delay would be determined by the RC time constant.

In this section, w briefly looked at applications, and then we looked at the effect of a long time constant, moderate time constants, short time constants. This completes section 7-4.