The Inverting Amplifier

TI's LMV722 operational amplifier, configured as an inverting amplifier, was used for this portion because of its great characteristics at low operating voltages. Calculation of the gain at which the op-amp is to operate at is realized through node voltage analysis. The actual amount of amplification needed to ensure that the device responded well to various intensities of sound was found through a trial and error process.

The key to finding the relationship between Vin and Vout of an operational amplifier is recognizing the following assumptions:

• No current flows into the inputs
• There is a virtual short between the Vn and Vp input pins
• The gain of the op-amp with no feedback is infinite
• There are a few more items such as infinite bandwidth, input/output impedance, and so on but they can be assumed to be already assumed ( If that makes sense =p )

Since I have chosen to operate the amplifier in the inverting configuration, the schematic and derivation will match as such.

Since the gain of an amplifier is defined as being "G = Vo/Vin" or "G = Vo/Vsig", the derivation should be as such to get the variables in that form. I started by making the assumption that if the amplifier is capable of infinite gain, it would be able to make the difference between its inputs, Vn and Vp, be 0v or otherwise seen as Vn = Vp. This brings forth the inference that since Vp is attached to virtual ground, Vn must also be at ground potential. From Vn, I can form the individual elements of the node equation by using the voltage drops across the resistors and the fact that the inputs do nothing to affect the nodes because no current flows into them.

So... from the bit of math above, it seems that the gain is dependent upon the ratio of R2 to R1. The negative sign indicates that the signal is inverted on the output of the amplifier with respect to the signal coming in. With this new found (not really) knowledge in mind, the amount of gain needed can now be found and easily applied. An interesting thing to note about the node voltage analysis method is that it actually uses the currents in the sense that each element forms the appearance of V/R.

Finding the Gain

The amount of gain needed to amplify the signal, from the microphone, to a large enough magnitude so that the analog to digital converter is fully utilized will depend on the environment it is operating in and the microphone used. By going ahead and prototyping the entire circuit, the amount of gain needed was found to be in the range of 200.

Although the amount of gain can vary from unity, that is a gain of 1, to in the 1000's, this amount affects other abilities of the amplifier such as bandwidth. Although I made the assumption of the operational amplifier possessing infinite bandwidth, the reality is that it is some finite number that can be referred to as being the "unity gain bandwidth" or the bandwidth when the operational amplifier is operated at unity gain. This number, a constant, is the product of the gain and the bandwidth at that gain. As a result, one can infer that raising the gain to 2 will cut the bandwidth in half.

Fear not though because for the operational amplifier I have chosen, the now effective bandwidth at a gain of 200 is 50 KHz. 50KHz is above the hearing range of human beings, maybe much more for those of you that listen to loud music 24/7, so it is more than acceptable a trade off.

Virtual Ground

A virtual ground is, in my definition, a voltage node that lies between Vdd and Vss and is sometimes used as a reference point for other devices in the circuit. The usage of such an "artificial" reference point stems from the fact that the audio signal after the capacitor needs to be able to swing above and below a reference point. If one were to select Vss as the reference point, the signal would not be able to swing to a more negative voltage than Vss. The cause for concern, even if we are only taking half the signal as shown later in this write up, is that the operational amplifier will be forced into saturation when trying to amplify the negative portion of the signal.

By creating a virtual ground that is one-half of Vdd, there is enough room for the operational amplifier to swing its output in both directions and decrease the possibility of saturation under most conditions. The virtual ground for this project was created by using a simple voltage divider that is composed of two identical resistors. Values of these two resistors should be high enough to avoid excess power drain on the battery and yet small enough to be of small impedance.

For further improvement, the virtual ground of this circuit can be made even more robust by placing capacitors between each rail and the virtual ground's output. In addition, an operational amplifier in a unity-gain buffer configuration can be used to decrease the impedance of the virtual ground. More information is located at a website called TangentSoft.