arigy said:
I've tried googling information on Howland Current Source noise, and found nothing but an article in International Journal of Electronics on Noise analysis of a Howland current source (http://testservice-eprints.gla.ac.uk/23847/). Unfortunately, this article is not available online, and I personally am not qualified enough to analyze it myself
A little too much to explain in a simple post, but not unlike noise analysis for general purpose opamp circuits.
Regarding practical implementation: as it is vital for Howland Current Source to have precisely matched resistors (order of 0.01%), it might be inconvenient for actual use. However, instrumentation amplifiers and balanced receivers are all already has matched set of resistors (0.05% generally) which we can easily use,
It is worth inspecting how vital that precision really is. Engineering is all about managing such trade offs. The target output impedance when making a proper current source is infinity. Most text book examples I saw started with meg Ohm range feedback resistors, then used the the CM balance to multiply that up higher. Of course we run into the practical limit to output current and noise. It doesn't take a sharp pencil noise analysis to realize 1M resistors are noisy. The practical design target is to deliver the same current as a simple summing resistor, but with much higher compliance or source impedance.
The undesirable characteristic of the virtual earth summer that we are trying to mitigate is the N+1 noise gain (with resistor inputs). If we re-write that equation for actual value of the current sources output resistance we get ((N x Rfeedback)/Rcurrent sources)+1. So for standard case of Sum amp feedback R = to input R the equation reduces to the familiar N+1. But now if we even just modestly raise the output resistance of the synthesized current source the noise gain drops a like amount. A current source with only 2x the impedance of a simple resistor will have 1/2 the total noise gain. !0x R will make one tenth the noise gain etc. In practice I was very happy to get a 20-30 dB improvement. Leave 100 dB matching to the bench tweakers. I was making consoles with hundreds of these.
and previously mentioned AN-1515 (Burr Brown also has an Application Bulletin on this, see fig.51
http://focus.ti.com/lit/an/sboa046/sboa046.pdf) also suggest alternative solution involving OpAmp voltage follower, which allows us to use only a single resistor for setting of current.
That is another way to skin the cat. I never saw that before but I guess it will work. I would be a little apprehensive about hanging a hundred opamp buffers (one per current source) on my sum bus. I guess with modern high performance opamps the bias and input noise current will be modest, but 100x a good number could add up. Not to mention cost of another 100 opamps. I guess we could buffer the buffers but now we have even more lag to worry about for stability. Note: we mainly care about the noise gain in the audible bandpass, so it's OK if the output resistance degrades a little at very HF, so we could probably compensate for the lag of at least one buffer without degrading the audio performance.
The problem is: different balanced receivers use different values of feedback resistors, and, if I understood correctly, it is better to have gain resistor value less then feedback resistors. If we stick to INA134/SSM2141, I suppose it is okay to have gain resistor of 10k (which will give us 1mA for 10V differential input). However, THAT1240, which considered a superior balanced receiver, has 9k resistors. Wouldn't 10k gain resistor too much for it? What bad will happen, if we change gain resistor, for example, to 4.7k (will give us 2.13mA for 10V diff.input)?
The math for that current source topology is pretty much independent of how the resistance values are parsed as long as the two legs have identical ratios. For good noise performance the values want to be kept relatively low. For good tracking and matching in production keeping it down to a handful of values is helpful.
FWIW, If I were to revisit this today using 30 years newer technology, and perhaps being less budget conscious, I would focus more on the actual opamp used than having precision resistors integrated in, unless it had all 5 precision resistors on board. As soon as you start mixing external with internal resistors, the matching of the combined result is no better than absolute value tracking of both and IMO suspect.
However, as I have already explained you don't really need .01% matching, so they could work, while it looks like perhaps an unnecessary expense vs. rolling your own from bare opamps and precision resistors.
JR
