Howland Current Source Impedance

 Here we derive the source impedance of the Howland current pump.  The ideal current source impedance is infinity.  The Howland current pump is depended on resistor matching.  We consider the effect of mismatch on the source impedance.

The source impedance is R3/mismatch, a result is given in AoE3, which appears to err on which resistor R3 refers to.

Assume the resistors are 0.1%.  The worst case source impedance is 250 times of  R3 in the diagram.  For small current on the order of 1mA, R3 is on the order of 5KOhms, the source impedance is about 1MOhms worst case, compared with LT3092, which has an output impedance of 100MOhms at 1mA and 2MOhms at 10mA.  

In the so-called "improved" Howland current source, a buffer is inserted to have a separate resistor to set the current.  We can similarly derive the output impedance.

If we assume R1=R2=R3=R4=Rs, the output impedance is Rs/(2*tol), which is twice as large as before.