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How Does The Howland Current Source Work?



Current source programs an output current as defined by the user, regardless of the load resistance. We know that when load resistance is larger, the voltage across it also increases. An ideal source would maintain a constant amount of current even if the load resistance changes, or in other words even if the output voltage changes. Such behavior describes a very good current source that has high output impedance. Remember, the output voltage changes, but very little or no change in output current. That means high output resistance or impedance. We use the term impedance when dealing with changes.
Howland circuit in the figure is a classic current source circuit.  When R1 is made equal to R2, RF equal to R3, the output current is given by VIN/R1 where VIN is V1 minus V2. A simple implementation is grounding V2 and taking V1 as the VIN.

Figure 1 Basic Howland Current Source


This circuit is such a clever manipulation of the op amp, such that the load current is made simply to be a function of VIN and R1. I am going to try and explain this circuit in an intuitive way as best as I possibly can. The load current is simply given by:


The VIN creates a current across R1 while a potential develops at the positive input terminal of the op amp. Observe that the load current is equal to this current plus the current flowing through R3. Observe also that the current that flows through R1 is VIN divided by R1, minus the current that would be produced by VA divided by R1. Here it goes:



If R1 is equal to R2, VA/R1 would be the same current as the one flowing through R2. 


We know that this same current flowing through R2 is equal to the current flowing through RF, which is IF. Now, hold on tight, if RF is equal to R3, then the voltage across RF is the same across R3. Therefore, that also makes the current I3 equal to the current IF. 


Going back to equation 1, we saw that the load current is the sum of the input current and the current through R3. Combining equation 1 and equation 2:


We see that if I2 is equal to I3, this is reduced to simply VIN divided by R1.

Stay tuned folks, there will be a second installment on this for the improved Howland current source.

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