# Equivalent Circuit of Howland current Pump

Why is at norton circuit for Howland current pump the current source is taken as vi/R1 instead of vi/R0? Because the formula for Norton current is IL=In*(Rn/(Rl+Rn))

• The purpose in doing the Norton equivalent is to illustrate the ideal current source of Vi/R1 with a non-ideal output resistance < $\infty$ when R2/R1 is not equal to R4/R3. You should be able to derive the equations shown, they are correct. – Spehro Pefhany Mar 23 at 5:58
• There are two Voltage sources, (not one) required to make this Norton source, namely, Vi & Vo. You can swap R1 and load positions, Now Vin controls load current source directly to a virtual ground from 2 sources. (Vin,Vo). basic Ohm's Law Io=Vi/load. You can even replace the gnd on R3 with Vin then a positive voltage creates a negative current to the load. Io=-Vin/R3 – Sunnyskyguy EE75 Mar 23 at 7:40
• If the current formula involved Ro, then it would be a poor current source. – Andy aka Mar 23 at 9:17