I'd like a basic force balance circuit that I can build on
Long ago, Wireless world published a flux gate force balance circuit using a loudspeaker as the position driver. Gargoyle probably knows - I don't have time just now to dig. I MAY have the magazine if someone finds the reference.

This amazingly simple but capable fluxgate magnetometer paper should be of interest. A cleaver sensor. I've seen similar suggested elsewhere - some superb results are claimed. Brown University. They say  - 


A simple ﬂuxgate magnetometer can be constructed out available equipment in the lab. It can easily
measure the magnetic ﬁeld of the earth .You will need the following equipment: (1) A function
generator,( 2) an oscilloscope, (3) Pasco waveform analyzer, (4) a Thorton ampliﬁer ,(5) a spool
of magnet wire, and (6) 1 meter of 18 gauge stovepipe wire( iron wire that becomes magnetically
saturated at low magnetic ﬁelds)




DIY fluxgate sensor and some good references. 

Example only magnetometer circuit from the above page. 





Brooke Clark's super sensor links page should be useful.



These people  who patented the circuit below think it's a force balance magnetometer based on a geophone:


The invention concerns methods and apparatus for improving the performance of a force-balance accelerometer based upon a conventional, single-coil, velocity geophone. Specifically, the operating temperature range is increased through the use of both a temperature-compensating reference impedance, and a new electronic circuit architecture. Two specific types of temperature-compensating reference impedances are disclosed. One is a pure DC-resistance, with the temperature coefficient of the DC resistance matching that of a single coil of a conventional geophone. A second reference impedance adds a series reactance which closely matches the ratio of total impedance to DC-resistance, and the temperature coefficient of this ratio, with that of the geophone coil.

A method is also described which provides for decreased magnitude of a reference impedance required in an accelerometer. This allows for a significant reduction in the physical size of the reference impedance. The reduction in size reduces the physical size of the impedance and the sensitivity of the accelerometer to external time-varying magnetic fields.






The "missing link" in the above which I could (easily :-( ) have made clearer is that a traditional geophone is a simple open loop device where a coil is moved near a magnet by a vibration source and induces a voltage which is analysed. Such instruments are affected by self resonance.

What Peter referred to and what the Wireless World article I mention addresses, was the use of feedback to null the position of the moving element against the perturbing forces and produce a feedback error signal as the output. Such a system is less affected by the mechanical characteristics of the sensor device. 

The WW circuit implemented a fluxgate detector to provide feedback. My mention of the magnetometer is in that context but I agree, taken in isolation, it is not clear how it relates. 

Finding the WW article would be nice. I'll try in due course. Anyone?