Talk:Circuit Idea/Reinventing the Famous Howland Current Source

Howland circuit
(a copy from the Wikipedia talk page about negative resistance) Circuit-fantasist (talk) 17:21, 4 March 2009 (UTC)

The circuit on Fig. 4.13 (The Art of Electronics, page 182) represents the first version of Howland current source (pump) or, if we exclude the input voltage source and the load, a Howland voltage-to-current converter. It consists of four ingredients: an input voltage source VIN, a negative impedance converter INIC (R1 = R4 = R3 = R and the op-amp), a "positive" resistor R2 = R and a load. The voltage source VIN and the INIC constitute a voltage source with negative internal resistance -R that is connected in parallel to the positive resistor R2 and the load. The role of the positive resistance R of the resistor R2 is to "neutralize" the negative internal resistance -R of the source. As a result, the final source has an infinite internal resistance and behaves as a constant current source.

The second version of Howland current source (see Fig. 1 of MAXIM's AN1155) consists of an input voltage source VIN, a positive resistor R, a load and a negative impedance converter INIC (R1 = R2 = R3 = R and the op-amp). The input voltage source and the resistor R constitute an imperfect current source with positive internal resistance R that is connected in parallel to the negative resistor INIC and the load. The role of the negative resistance -R is to neutralize the positive internal resistance R of the source. As a result, the load is driven again by a constant current source with infinite internal resistance. Well, let's include some algebra to be more cogent.

The imperfect current source produces a current IL = (VIN - VL)/R = VIN/R - VL/R. As you can see, it differs from the ideal result IL = VIN/R by the term VL/R. It is more than obvious that we may compensate this error by adding the same term; then, IL = VIN/R - VL/R + VL/R = VIN/R. That means to inject an additional "helping" current IH = VL/R that is proportional to the load voltage. What is this circuit that can produce such a current IH? Of course, it is a voltage driven negative resistor with resistance -R; it is a negative impedance converter with current inversion (INIC) that is connected in parallel to the load.

The generalized version is a combination between the two ones where the output current is proportional to the difference between two input voltages. As a conclusion, Howland voltage-to-current converter consists of two connected in parallel resistors with equivalent but opposite (positive and negative) resistances; Howland voltage-to-current converter = INIC + resistor. The "neutralization" between them produces an infinite resistance and, as a result, a constant current. The circuit is stable since the positive load resistance remains after the "neutralization" (another wisdom: the positive resistance has to dominate over the negative resistance to have stability).

Deboo integrator (see again Fig. 1 of MAXIM's AN1155) is just a Howland voltage-to-current converter driving a capacitive load; Deboo integrator = Howland voltage-to-current converter + capacitor. It has two advantages over the dual inverting integrator: it is a non-inverting circuit and the capacitor is grounded. But it has two disadvantages as well: it requires an op-amp with differential input and it has a bigger error depending on the resistor tolerances (here, the op-amp does not monitor the result of the compensation as it monitors the virtual ground at the inverting circuit).

It is interesting that although there was nothing new in a Deboo integrator (actually, it was just a Howland pump driving a capacitor) Deboo was not aware of the Howland current source when he invented his integrator. I found out this fact in a personal correspondence between me and Deboo a year ago (Deboo was impressed by my comments to an EDN article about his famous circuit and emailed me). By the way, then I also exchanged interesting thoughts with Deboo about the unique feature of negative feedback to reverse the causality in circuits (to swap circuit inputs and outputs). For example, the negative inductance circuit is based on this idea.

Today, I found an extremely interesting source about the invention of the Howland circuit. Although it is nameless, it seems it is written by the very Howland. Circuit-fantasist (talk) 16:46, 1 March 2009 (UTC)

How to create simple negative impedance elements
(a copy from the Wikipedia Archive_4 talk page about negative resistance) Circuit-fantasist (talk) 17:21, 4 March 2009 (UTC)

I have started the most interesting part of the article where we have to show how to create negative impedance elements. I have exposed in detail my viewpoint at the topic in the full version of my suggestions for improving the article. Here, I will show the truth about these odd, mystic and never explained circuits by using extremely simple and clear explanations that are obvious for every thinking human being. Please, do not put a damper on my enthusiasm; instead, just help me to reveal the truth! Here are the main points:


 * True negative impedance elements do not exist in nature; so, we have to create them


 * The basic idea: to "copy" the voltage drop across the "positive" impedance element (by a voltage follower) and to add an equivalent voltage to the input voltage


 * Putting in practice the idea: making an op-amp produce a "mirror" voltage by using a negative feedback. Revealing the role of the op-amp in all kinds op-amp inverting circuits witn negative feedback. Circuit-fantasist (talk) 11:00, 29 January 2009 (UTC)