# Amplify coil antenna signal

Suppose I have a coil antenna that receives an ideal 100kHz ~200uVpp signal which I would like to measure. Can this signal be amplified to 2Vpp (10,000x gain) with 1% error for moderate cost (< $10)? What specs/variables should I be considering in order to determine the feasibility of this? Also, would using a resonant capacitor help amplify the received signal, or does it only serve as a filter to remove other signals? If this is not possible, what is a ballpark combination of frequency, gain, and percent error that could be comfortably achieved for$5-10?

If you are willing to calibrate each unit and then run it over a controlled temperature range, what you want should be doable.

The biggest issue is no the gain error, but maintaining good signal to noise ratio.

"Resonant capacitor" makes no sense, but resonance can be useful if the bandwidth of your signal is known and limited. This is usually the case when receiving radio transmissions.

At 100 kHz you can amplify the signal directly without fancy stuff like mixing with a intermediate frequency, then amplifying that. A LC resonant filter or two in the chain would be useful to reduce the gain at frequencies you don't care about.

A 1 GHz gain bandwidth product opamp should easily provide an amplification of 10,000 with high tolerance resistors. However, the devil is in the detail and I would suggest that two cascaded stages having gains of 100 each (using opamps with 100 MHz gain bandwidth product) would be more feasible.

However, if all you wanted was a controlled 2 volt p-p output you could build a variable gain amplifier with feedback that ensured the output remained at an accurate 2 volts across a reasonable range of inputs centred about 200 micro volts.

It's not clear to me whether you want A or B.

Trying to resonate the coil will magnify the signal at the expense of output impedance increasing substantially. Practical limits based on experience in metal detector design suggests you could get an amplification of 30 without incurring too much drift with temperature and, importantly, you'll get a several fold improvement in signal to noise ratio.

• I am looking to measure the amplitude of the signal, with 200uVpp being the lower bound of expected amplitude. – abc Jun 12 '17 at 18:47
• You need to be careful in your coil design if ultimately you are trying to infer magnetic field values. Just an observation reading between the lines. You also need to state your maximum signal too, to avoid amplifier saturation. – Andy aka Jun 12 '17 at 19:00
• Okay, yes there is the possibility of saturation. At this point I am just trying to understand the accuracy/resolution of the worst possible case to see if this method is feasible for the application. – abc Jun 12 '17 at 22:25

Here is topo using input analog multiplexer to calibrate the gain; ENOB Effective Number Of Bits is only 5.5, or approximately 50:1 accuracy, due to thermal noise floor.

7.8mV of the output KT noise is from that MUX; another 7.8mV from Rgain (100 ohms) in the DC-blocking series RC of non-inverting gain opamp topology (both stages use that topo, to avoid DC-offset buildup). And 6milliVolts from the first opamp (OPA211). The 2nd opamp is MCP655, a 50MHz opamp.

Here is the wide, tho DC_blocked, frequency response. Notice the resonance out at 10MHz, where the coil/sensor inductance peaks with capacitance of the analog multiplexer.

Regarding ERROR: neither opamp has satisfactory 1/GH accuracy at 100KHz, hence I suggested you consider calibration (one time). Another choice is 3 or 4 stages, with gain of 80db/3 (~ 21x) or 80dB/4 (10X).

To lower the noise floor, get rid of the analog multiplexor, reduce the stage#1 gain set resistors from 101_ohm and 10kOhm to 25_ohm and 2,500 ohm. Keep the OPA211 for its 1nanoVolt/rtHz noise density.

Finally, what is your interference environment? For 1% error of 200uVpp, the total injected trash (Efield, Hfield, VDD, GND) must be 2uV ReferredToInput.

Any black-brick battery charger within 10meters should be suspect.