# Digitally controlled smoothly variable gain?

I have a circuit that outputs about 600mVpk wave shape. I need to be able to output between 10mVpk to 10Vpk accurately, preferably with no calibration but a known error. The whole process should be supervised by digital means.

The general scheme I was thinking about is amplifying the signal to 10Vpk and some attenuation device to set different gains. This could be a series of resistive dividers that can be inserted in line. Each one is attenuating the signal by a different amount like -2dB,-4dB,-8dB,-16dB and they can be combined to create more attenuation points like -6dB or -30dB. This can be done using 4 SPDT relays but this is not enough. What additional element can I use to make up the spaces. I would like a high resolution. Possibly 10mV if possible.

• Use a multiplying DAC? – Dave Tweed May 8 '14 at 15:33
• @Dave: You should make that a answer. I'd upvote it. – Olin Lathrop May 8 '14 at 16:17
• What's the highest frequency component of the signal? If it's audio you could use a digital pot, higher frequency an MDAC, higher again and some other method such as switched attenuators will have to be used. – Spehro Pefhany May 8 '14 at 17:26

As Dave Tweed commented, a multiplying DAC (MDAC) seems the way to go. You don't mention your digital interface, frequency range or your output power requirements, so some details you'll have to work out for yourself. Analog Devices makes a wide variety of MDACs, which go all the way up to 16 bits resolution, which would give you amplitude steps of 150 microvolts. See, for instance, http://www.analog.com/static/imported-files/circuit_notes/CN0055.pdf

As to your "no calibration" requirement, I doubt if that's going to happen. Assuming you want accuracy equal to your resolution, this implies an overall gain of up to about 16, with a gain accuracy of 0.1% (10 volt max / 10 mV resolution). This in turn suggests that your external gain components will need at least 0.05% accuracy, and this will not come cheap. You'd do better to allow some adjustment. This assumes that by "calibration" you mean "adjustment". If you use lower-tolerance parts and accept the resulting inaccuracies, you'll still need a calibration cycle in the sense of putting in various input levels and measuring the resulting outputs.

• Wow I totally forgot about these! This app note seems almost perfect for my needs. The output of this system in 50 Ohm terminated so it should have enough juice to put 10Vppk on that load. Freq. range is under 1Mhz. – user34920 May 8 '14 at 17:24
• Eeek! 10 volts into 50 ohms? Not with that op amp, you won't. Assuming your 10Vppk is +/- 5 V (not 0 - 10 V), you can series terminate with 50 ohms, and your actual output (at the amplifier) will be +/- 10V @ 100 mA. This will require a serious output stage. If you don't terminate the output as suggested, an accidental short on the output will quite possibly kill your amp. – WhatRoughBeast May 8 '14 at 17:56
• I did not think of using the op amp shown at the application note, but the idea is still the same. Off course a series fuse + protection diodes will also be placed at the output. – user34920 May 8 '14 at 18:47

I'm assuming you have a stable "reference" wave-shape that you can feed into a precision rectifier circuit. From this, you can obtain the peak value (or rectified mean value if that is more suitable) of that wave-shape. If you then use a linear attenuator such as from a JFET or analogue multiplier you can "pot" the AC amplitude down by a suitable amount.

This new output will be shaped like the reference waveform but not have a very precise amplitude ratio to the reference - there will be an amplitude error BUT, using the same design precision rectifier circuit, you can measure the attenuated signal and calculate the imprecise ratio.

The next thing to do is to make a correction to the JFET or analogue multiplier. This would be based on making the ratio error as small as possible. Now, you have a self calibrating system that relies on: -

• the control an analogue multiplier/attenuator with a DC value
• the accuracy/linearity of a precision rectifier
• the accuracy of being able to differentiate DC levels representing the reference and attenuated waveform.

Because you are dealing with DC values you can choose to go to 24 bit ADC technology to get very high resolution or just stick with analogue control.

Just a thought.