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Background

 This simulation  is intended to help you visualize the types of  phase shift that occur in circuits as the relationship between circuit components changes. Download rlc.zip and copy it to a convenient place on your hard drive. Unzip it to obtain rlc.exe. When you execute this file, the program will start.

 All component values are initially set to 1.0 (W, uH, and uF, respectively). The angular frequency, w, is fixed at 10⁶. You will note that this is the resonant frequency under these conditions. Component values can be changed by the sliders across the top and the values are shown in the text boxes at the right. The total impedance and the phase angle are also shown at the right, and the system is at resonance when the components are selected such that the phase angle is zero.

 The schematic of the basic series RLC circuit is shown at the left. The circuit simulation can be set up for either constant current input or  constant voltage input by the selection buttons at the lower right of the window. The check boxes across the bottom select what is displayed. The options include the voltage across the resistor (V(R), green), the inductor (V(L), yellow), and/or the capacitor (V(C), blue). The input current ((I(in) in mA) and the total voltage (V(in), which is the sum of the other three voltages) can also be displayed. The white curve is always the constant input variable (voltage in or current in) and the red curve is the other input.

This simulation can be complicated to get into, so you might find it convenient to start with the following sequence. After completing this sequence, you can play with the simulation in other ways that interest you.

 First Step

Start with the input set to constant current. Set all component values to unity. Select I(in), V(R), V(L), and V(C) for display. You probably see only three curves, and either the white or green one is missing. Why? Because the voltage across the resistor and the current are always in phase with each other. With these component selections, their magnitudes are also equal. So the curves lay on top of each other. Now deselect the I(in) curve for display.

 Note how the V(C) curve lags the V(R) curve by 90 degrees and how the V(L) curve leads the V(R) curve by 90 degrees. Note that these phase relationships will not change throughout this entire simulation. The voltages across these three components will always maintain this phase relationship no matter what values the components are set to. 

Note how the V(C) and the V(L) curves are exactly equal in magnitude and opposite in phase. Their sum is always zero. That is the definition of resonance. That is why, under these component values, V(in) is exactly equal to V(R). 

 Change the value of R. The voltage V(R) changes in response. Why doesn’t V(L) or V(C) change? Because the input is constant current. Therefore, a change in the value of the resistor doesn’t change the current. Therefore the voltage across the other components doesn’t change. Reset the value of R back to unity.

 Add V(in) as a selection for viewing. Change the value for C. Note several things. The voltage V(C) changes. Therefore V(in) changes, since V(in) is the sum of V(R), V(C) and V(L). The phase relationship changes, since we are no longer at resonance. The V(in) curve shifts in phase relative to I(in). Why doesn’t V(R) or V(L) change? Because we are still dealing with constant current in, and since their component values are not changing, the voltage across them doesn’t either. 

If the phase relationship is changing, why don’t the curves shift relative to each other or to the vertical axis? Because we are dealing with constant current in. Therefore, V(R) is always in phase with I(in) (which is constant) and the other two voltages are always 90 degrees shifted in phase from V(R).  Reset all component values back to unity.

Second Step

Clear the check boxes for V(R), V(L), and V(C) and select the boxes for V(in) and I(in). If all component values are set exactly to unity, you probably see only one curve, not two. Why? Because when the component values are set to unity, the voltage and the current have the same magnitude. And since the system is at resonance, they have the same phase relationship. Therefore, they superimpose exactly on top of each other.

 Now change the value for R. Note how the input voltage changes in proportion to R. Remember that the input current is constant, so less voltage is required for smaller resistance. Note how the phase relationship does not change simply because R is changing. Reset R to unity.

 Decrease the value for C a little. Note that the voltage curve shifts to the right and the phase angle display shows a negative number. Why? Because voltage lags current when the circuit is capacitive. Note that the voltage peak occurs later than (lags) the current peak. Decrease the value for the inductor. The voltage curve continues to shift. Move the inductor and capacitor sliders all the way to their minimum positions, and select the x10 button to change the display scale. Note how the voltage curve lags the current curve by almost 90 degrees (the text box probably says something close to –84 degrees). This can be seen by comparing the position along the horizontal (time) axis of the peak of the voltage curve and the zero-crossing of the current curve.

 Change the L and C settings to their other extreme. Note that the phase shift changes from almost –90 degrees (lag) to almost +90 degrees (lead).

Third Step

Reset the component values back to unity and set the input condition to constant voltage. You may only see one curve, since with unity values (resonance) the V(in) and I(in) curves will be equal in magnitude and in phase. Note that the V(in) and I(in) curves have changed color. The white (constant) curve now indicates the voltage in.

 Change the value for R. Note that input current changes inversely with R (since we now have constant voltage in). The phase relationship doesn’t change because the LC circuit is still in resonance.

 Change the value for C. Note that the phase relationship changes, and as C decreases current begins to lead voltage (and correspondingly, voltage lags current). Reset all component values back to unity.

Fourth Step

Deselect V(in) and I(in) for viewing, and select the other three voltages. Change the value for R. Note that V(R) does not change, but V(C) and V(L) both do. Why? This is a good question. First, with unity component values, V(C) and V(L) are at resonance, so their voltages are equal and opposite and cancel. So V(in) equals V(R). And since V(in) is now constant, so must V(R) be. But as R changes, I(in) must change. As I(in) changes so do V(C) and V(L) change in response, but they change together, so that they are always equal and opposite and cancel.

 Reset R to unity and begin to reduce the value for C. As C gets smaller, the voltage across it, V(C), increases. Since the total voltage is constant, the voltage across V(R) and V(L) must both decrease. That means Z must be increasing so I(in) is decreasing. Watch the values for Z and the phase angle in the text boxes.

 The curves shift to the left, but they are all shifting exactly in the same phase. Remember, the phase relationship between V(C), V(L), and V(R) never changes.

This simulation allows you to visualize what is meant by phase shift and to see what it is that is shifting with respect to what else. Experiment with other combinations of component values and input conditions and then try to understand (and explain) what happens.

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