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 R_2, R_F equal to R3, the output current is given by VIN/R1 where V_IN is V₁ minus V₂. A simple implementation is grounding V₂ and taking V₁ as the V_IN.

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 V_IN 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 V_IN 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 V_IN divided by R₁, minus the current that would be produced by V_A 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 R_F, which is I_F. Now, hold on tight, if R_F is equal to R₃, then the voltage across R_F is the same across R₃. Therefore, that also makes the current I₃ equal to the current I_F. 

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 V_IN divided by R₁.

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

If you liked this, please click the like button, as a way of saying thank you, to help me get more motivated,  improve this and also help share this to other people.