An in-depth look at phase shift in analog circuits

This article will discuss phase shift, the effect of a circuit causing the voltage or current to lead or lag from input to output. In particular, we will focus on how reactive loads and networks will affect the phase shift of the circuit.

We will look specifically at how phase shift affects an otherwise perfectly reliable op amp, and how reactive elements can be used to our advantage in certain resonant network topologies.

Capacitive load on buffer

Below is an op amp acting as a simple buffer.

Figure 1. A basic buffer or "voltage follower" using the LF411 op amp.

The response is uniform and flat up to 1 MHz before the phase begins to decrease.

Figure 2. Output response of the LF411 voltage follower. It starts attenuating the signal at about 4 MHz.

This circuit relies on negative feedback (non-inverting output to inverting input), and -180° phase shift causes negative feedback to become positive feedback (180° phase shift output to inverting input).

Now let's try loading the circuit with a capacitor.

Figure 3. Using a buffer to drive very large capacitive loads. This is not a good idea!

If the op amp has a resistive output impedance, which for this op amp (LF411) is about 0.1 - 10 Ω at unity gain, we would expect the capacitor to cause a -90° phase shift above the cutoff frequency. Let's see what happens.

Figure 4. Evidence of a bad capacitor: the amplifier starts to oscillate!

That looks bad. The amplitude response has a resonant peak and the phase drops rapidly to -180°, which is a perfect oscillation method. There must be at least three capacitors (inductors unlikely) causing these response changes. With our suspect in hand, we can walk through the circuit and find out exactly what's causing the problem.

Phase shifting using reactive networks

Phase shift becomes particularly important in circuits such as feedback networks, resonant networks, and oscillators. We may want to have a 90° phase shift in our circuit to intentionally control the phase. Quite simply, we can add a capacitor (or for the adventurous, an inductor) to shunt the output and see where we stand.

In fact, we may not want only a 90° phase shift on the load. Maybe we want 180°.

Maybe we just need to put in a second capacitor?

Figure 5. Innocent attempt to create a 180° phase shift

This won't work - two capacitors in parallel just form an equivalent capacitor. They all share the same voltage, so they can't all contribute different amounts of hysteresis. We need to be more creative.

One way to achieve this effect is to use a multistage RC filter. But a more ideal approach might be to separate the capacitor from one or more reactive components, as shown in the circuit below.

Figure 6. To solve the problem, this circuit should have a 180° phase shift at resonance.

This circuit is a low-pass filter that will resonate at the same frequency as a resonant network consisting of a 1 µF capacitor and a 0.5 µH inductor (or a 0.5 µF capacitor and a 1 µH inductor).

Figure 7. Bode plot of CLC network showing good resonance and fast phase changes.

From the response and phase shift we can see that the circuit behaves like an RC filter with the source resistor and two capacitors in parallel, reaching -90° shortly before the resonance peak. Then a resonance peak occurs and the phase drops sharply to -270° (the maximum phase shift of the three reactive elements). Exactly at resonance, the phase shift is the desired 180°.

This circuit is used as the resonant element in the Colpitts oscillator, while the inductor-capacitor-inductor variant is used in the Hartley oscillator. Typically, the circuit will be drawn as shown in Figure 8.

Figure 8. Alternative diagram of the CLC circuit commonly seen in Colpitts oscillator schematics.

Although it may slightly confuse the purpose of the elements, drawing the elements as Figure 8 gives the appearance of a single resonant element. You can see an example of a Colpitts oscillator with a resonant network drawn in this way in Figure 9.

Figure 9. Typical diagram of Colpitts oscillator

The last two examples strike some chords. Because resonant elements rely on the ability of reactive elements to provide phase shift, it would be illustrative to say a little more about phase in a resonant circuit.

Simulated resonant tank

When the reactance of the inductor and the reactance of the capacitor are equal, resonance occurs in the series LC circuit. At this point, the inductor and capacitor share the same current; ideally, the inductor provides a +90° (leading) voltage phase shift, while the capacitor provides an ideal -90° (lagging) voltage phase shift, meaning that the voltages across the circuit are different. Phase 0° (no voltage drop, short circuit). A similar effect creates an LC resonant circuit.

But as we now know, capacitors and inductors only provide +/- 90° of phase shift when the source or load impedance is set correctly. Take this resonant tank as an example.

Figure 10. A simple resonant tank powered by a 1 Ω output impedance. Will it ring?

The source impedance is only 1 Ω and the load is 10 kΩ. The tank should resonate at 5 kHz. We can test for resonance by applying an input step and looking for ringing. The simulation results are as follows.

Figure 11. The tank response is too damped to allow any ringing, which is desirable in many situations.

The tank didn't seem to make much noise. The reason is the source impedance, which is too low considering our L and C values. We want our capacitors and inductors to allow energy to be exchanged back and forth quickly at the resonant frequency, but this effect is suppressed because the resonant tank Q-factor is too low.

There are several ways to understand this. In the context of phase shifts, we might propose the following explanation. Looking only at the source impedance and capacitor, we see that they form a low-pass RC filter with a cutoff frequency of 160 kHz. Instead, the source impedance and inductance form an RL high-pass filter with a cutoff frequency of 160 Hz.

If we agree that the behavior of the resonant tank depends on the phase shift provided by the components (-90° voltage phase shift from the capacitor, +90° voltage phase shift from the inductor), then the reason for damping becomes obvious.

An RC low-pass filter will provide a -90° phase shift above its cutoff frequency, while an RL high-pass filter will provide a +90° phase shift below its cutoff frequency. The resonant frequency of 5 kHz is too high for an RL filter to provide positive phase shift and too low for an RC filter to provide negative phase shift.

Reasoning this way, we induce ringing in the circuit by changing the values ​​of L and C (decreasing the inductance and increasing the capacitance by an equal amount) or by changing the source impedance.

Increasing the source impedance has the desired effect.

Figure 12. When the source impedance is 100 Ω, the resonant frequency is 5 kHz.

Now, as expected, the slot ring rings with a period of 0.2 ms (corresponding to a resonant frequency of 5 kHz).

in conclusion

This article takes a closer look at phase shift in analog circuits. Our topic took us through various circuits: amplifiers, filters, resonant tanks and oscillators. Capacitors and inductors will always cause phase shifts, but their effects are affected by the source and load impedances. Here we mainly assume that the source and load impedances are resistive. However, the reactive element is always present.