The common-base (CB) BJT configuration is the second stage of cascode amplifiers. It is useful as a voltage translator to the high side of an amplifier with a large voltage range. This article addresses the question of how the RB, CB combination at the base node affects the frequency response.
The base is usually bypassed to ground by a capacitor, CB, to keep the base voltage constant. This CB is usually added when the external circuit resistance at the base node, RB, is appreciable. The CB stage contributes to the frequency response of the overall amplifier. Within feedback loops, its effect on the loop gain is of interest.
To give the question a concrete context, consider the following fragment of a feedback amplifier in which an op-amp drives a CB stage.
Both Q2 and Q3 are CB stages, but Q2 is the CB stage of interest. It has a base node resistance of about R29 (RB) and base capacitance of C27 (CB).
The commodity “voltage-feedback”op-amp has a bandwidth (open-loop) of fbw, a relatively low frequency. For an op-amp voltage gain of K = 50 k, the dominant-pole gain at fbw decreases at a log-log slope of –1 until it intersects a gain of one at fT (the gain-bandwidth product). For an LM358 (the LM392 is half LM358 or a fourth LM324) fT of 1 MHz, then fbw ≈ fT/K = 20 Hz. (These parameters are also typical of many commonly-used BiFET and CMOS op-amps of more recent design.) If all the other poles and zeros in the loop are much greater than fbw, then the op-amp response can be approximated as having a pole at the origin. The op-amp provides almost all of the loop gain and the feedback loop can most easily be stabilized by this low-frequency op-amp pole. Additional poles in the loop can cause the phase of the loop gain to diminish the phase margin of stability and require compensation by the addition of zeros.
Alternatively, if the op-amp pole is made even lower in frequency by placing a capacitor between pins 1 and 2 of U1A, then this dominant-pole compensation technique causes the higher-frequency poles to be separated from the dominant (low-frequency) pole to such an extent that the loop gain reaches a safe value of one before the delaying effects of the phase from the higher-frequency poles can significantly reduce phase margin.
What can spoil this dominant-pole scheme are spurious zeros in the loop. A zero has the opposite effect of a pole and causes the gain to increase, thus sustaining it above one to a higher frequency. This allows higher-frequency poles to more adversely contribute phase effects and reduce phase margin.
Suppose a zero were to appear at a frequency of zB = 1/RB•CB caused by the CB stage. Then the –1 gain-magnitude slope on a Bode plot will cease rolling off at zB and remain constant until the next higher pole resumes a –1 roll-off of gain. Upon reaching a now-higher fT, the zero might have shifted it enough so that a third pole can cause the loop phase margin to be inadequate and make the loop unstable. The magnitude plot is shown below.
The solid plot is the frequency response of the op-amp. The op-amp alone contributes –90 degrees of phase delay at fT from its single pole. Any poles less than 10•fT will contribute significant additional phase delay. A phase-lead response of a zero and pole for which z < p will result in the extension of the gain roll-off as shown by the dashed plot. Because the new fT is greater than the op-amp fT by a factor of pB/zB, additional high-frequency poles can increase the phase delay. Between zB and pB, the zero increases the phase margin of stability, but if more than one higher-frequency pole decreases the phase (at fT), then the added phase margin of the zero is more than negated; the amplifier is less stable.
The CB stage base circuit can contribute a phase-lead effect as shown in the plot. The base circuit can be referred to the emitter by applying the β transform (zE = ZB/(β + 1)). The resulting equivalent circuit is shown below.
Then the CB transconductance follows from straightforward application of passive circuit analysis:
The zero and pole are at Bode-plot (positive) frequencies
For positive R and C element values, z < p because without the shunting effect of RE + re, p = z. The shunting effect lowers the resistance, causing the pole to be at a higher frequency.
The above amplifier circuit fragment can now be analyzed to find the effect of the CB circuit on its response. The typical PN2222 quasistatic β ≈ 149 (so that β + 1 = 150). The op-amp voltage-range extremes for cascode operation are given and if we take the midrange value of 2.7 V and calculate the static IE(Q20), it is
Add re’ ≈ 0.6 Ω (which does not matter here but could in fast circuits) and the resistance in the emitter circuit is close to RE + re + re’ = 1012 Ω. When the base elements are referred to the emitter by the β transform, their values become
The zero and pole calculate to be:
In this CB-stage design, z ≈ p and the loop response is affected negligibly. This is a result of keeping the emitter resistance large so that its shunting effect on the referred base resistance is small: RE + re << RB/(β + 1).
It is a general design practice to not allow emitter resistance to become too small if linearity and stability are important criteria. The CB analysis shows that if RE + re << RB/(β + 1), then significant phase-lead is introduced by CB. This effect can also be used to advantage as a phase-lead compensator, though not usually with dominant-pole stabilization. Higher bandwidth can be achieved by not stabilizing with a dominant pole and using the CB phase lead effect to improve phase margin when z compensates negative phase shift of additional loop poles close by z, and p is much higher than those poles.
Note too that the pole, p, depends on β which can vary widely for typical discrete BJTs of the same type. This dependence decreases to the extent that RE + re dominates over RB/(β + 1). A larger CB reduces both z and p, but to reduce the phase and magnitude effects of z and p, make RE + re >> RB/(β + 1). Then z ≈ p, and pole-zero cancellation occurs. If z and p are not quite close enough to effectively cancel, they form a doublet and the phase response will have a positive “bump” in it toward greater phase margin. Not only does this put a positive bump in the frequency response, it also will add to the step response a corresponding bump. For the doublet to have a significant effect, however, z and p need to be a significant fraction of a decade apart.