In this article, we will discuss how shunt capacitance can be used to achieve frequency compensation in op amps and we will also see why this is not the preferred technique.
In a recent article on op amp frequency compensation, we discussed what the concept of frequency compensation is and how we can evaluate the stability of an example circuit. We conclude this article by addressing the concept of dominant pole compensation and how it was necessary to modify the open loop gain to allow for a profile that is dominated by only one pole.
Here, we will show a method to achieve this, known as shunt capacitance. Shunt capacitance compensation involves intentionally adding capacitance in parallel with the existing capacitance of one of the nodes in the circuit.
Compensation through a shunt capacitance
A brute force way of making a pole dominant is to intentionally add capacitance to the node responsible for the lowest pole frequency.
In the previous article, we introduced the two-pole op amp model from Figure 1 below, where F1 It is the lowest pole frequency.
Figure 1. Approximate AC model of an operational amplifier.
We then use the PSpice circuit in Figure 2 to generate the graphs in Figure 3.
Figure 2. PSpice circuit to plot closed-loop gains in 20 dB steps determined by R4.
Figure 3. Closed-loop gains of the circuit of Figure 2 for different amounts of feedback.
These graphs indicate that the op amp must be frequency compensated to avoid peak gain from occurring, especially at lower closed loop gains.
Once we decide where to put the crossover frequency ƒX For the unit profit operation, we find the new value of ƒ1 exploiting the constancy of the gain bandwidth product of compensated gain, or a0׃1 (new) = 1׃Xgiving like this
$$ f_ {1 (new)} = frac {f_ {x}} {a_ {0}} $$
Equation 1
A good starting point is imposing. Æ’X = Æ’2 Because it is easy to visualize geometrically.
For the circuit in Figure 2, we obtain Æ’1 (new) = Æ’2/a0 = 2,546 Hz, and we find the required value of the compensation capacitance dodo (to be placed in parallel with do1) leaving 1 /
The[2Ï€R1(DO1 + Cdo)]= Æ’1 (new), what gives dodo = 62.51 nF.
Running the circuit of figure 2, but with dodo Added as in Figure 4 (below), we get the graphs of Figure 5. Except for the unity gain case, all profiles are now spike-free because each enjoys a 90 ° phase margin.
Figure 4. PSpice circuit to plot closed loop gains in 20 dB steps after shunt capacitance compensation.
Figure 5. Closed-loop gains of the circuit in Figure 4.
Comparing Figure 5 with Figure 3, we see that the price to get rid of spikes is very low open loop bandwidth. In fact, the open loop bandwidth Æ’1 It is reduced from 6,366 kHz to 2,546 Hz.
The small number of peaks per unity gain response is due to the fact that allowing ƒX = ƒ2 we are imposing an ROC of 30 dB / dec, which implies a phase margin of φmeter ≈ 45 °. If a major φmeter is desired then ƒX should be placed under ƒ2 such that
$$ f_ {x} = frac {f_ {2}} {tanφ_ {m}} $$
Equation 2
For example, for φmeter ≈ 65.5 °, which marks the beginning of the peak, we must impose ƒX = ƒ2/ (tan 65.5 °) = ƒ2/2.194. Consequently, we need dodo = 62.51 × 2.194 = 137 nF, and we obtain ƒ1 (new) = 2,546 / 2,194 = 1.16 Hz.
It’s important to understand that shunt capacitance compensation is attractive from a pedagogical point of view, but that’s about it. Not only does it cause a dramatic reduction in bandwidth, but it also slows down other dynamics, such as spin speed and total power bandwidth. We will discuss a more practical and more used method in the next article on Miller Frequency Compensation.
Now that you understand a method of achieving frequency compensation in an op amp, let’s talk about a much better alternative, Miller compensation, which is discussed in the next article.
