One of the main reasons to use this circuit is to balance the currents between multiple channels such that the output current, and resulting heat dissipation, is approximately the same for each channel. This prevents distortion issues that could otherwise occur as amplifiers dip in and out of current limit or even thermal shutdown from uneven load sharing. Therefore, it is worth exploring the current mismatch equations for each of the two approaches. Here, we will only be considering two channels at a time, and will disregard the losses through the feedback path as negligible. Consider the expression for the mismatch current for a conventional buffer circuit (the circuit shown in Figure 1-1).

Note the expression is fairly straightforward, and exhibits a strong dependence on the proper matching of the trace and ballast resistances between the two channels. Compare this to the same expression for the parallel improved Howland pumps (the circuit shown in Figure 1-2). Let M_x = R_ballastx + R_tracex, N_Px = $\frac{R_{inPosx}}{R_{inPosx}+R_{fPosx}}$ , N_Nx = $\frac{R_{inNegx}}{R_{inNegx}+R_{fNegx}}$ , and L_x = $1-\frac{R_{tracex}*N_{Px}}{M_x*N_{Nx}}$ , where “x” represents one of the two channels under consideration.

There are three main kinds of loss in the parallel pump circuit – the loss due to the offset mismatch, the losses related to the V_p term, and the losses related to the V_load term. As long as the gain of the inverting path is equivalent to that of the noninverting path for each amplifier channel (that is to say, N_Nx = N_PX), then the V_load term will not contribute any error. If the above condition is met and additionally, the gains of the two channels are matched (N_N1 = N_P1 = N_N2 = N_P2), then the mismatch due to the V_p term will be dependent on how well matched the ballast resistances are (R_ballast1 = R_ballast2 for zero loss).

When the gain of the inverting path is equivalent to that of the noninverting path for each amplifier channel (that is to say, N_Nx = N_PX), then the loss due to the offset becomes $\left(\frac{V_{os1}}{N_{N1}*R_{ballast1}}-\frac{V_{os2}}{N_{N2}*R_{ballast2}}\right)$ .

Logically N_NX * R_ballastX < R_traceX + R_ballastX (since N_NX < 1), and so the parallel improved Howland pump circuit will be more susceptible to mismatches caused by offset than the conventional buffer circuit. However, when the losses due to the V_load and V_p terms are considered, it becomes clear that in certain cases the parallel improved Howland pump approach will balance the currents better than the normal parallel buffer approach (so long as the gain setting components of each channel are properly matched). This is most prevalent in cases where the trace impedance is high and the ballast resistors are mismatched, or when the difference of the trace impedances of the two channels approaches or surpasses the size of the R_ballast.

Recall there is an underlying assumption that the R_ballast resistance is small enough (relative to the R_fPos and R_fNeg resistors) that the loss through the feedback path may be neglected. This may be accomplished by using large resistors in the 10s of kΩ for the feedback path and/or using small ballast resistors.