FlexAnalog Using the Multiplier CAM

App Note AN302 (636 kB, 1 pdf file): Auto Nulling of Operational Amplifiers

Introduction

The library of Configurable Analog Modules (CAMs) provided as a part of the AnadigmDesigner®2 software allows the analog design to be abstracted at a higher level than transistors or discrete components. Now, designers can define their design in terms of gain stages, integrators, rectifiers etc., wire up the appropriate stages and implement the design in an integrated FPAA.

One of the more popular CAMs available within the AnadigmDesigner®2 Software library of CAMs is the ‘Multiplier’ CAM that allows the user to multiply two analog signals. This design brief illustrates how such a non-linear function is implemented in the FPAA. It also details some of the more important aspects of obtaining the maximum performance from this CAM.

Overview

The Okika Devices FPAA device family is based on switched capacitor technology. This is a linear technology, which says that the transfer function of a given CAM is NOT a function of the signals being applied to it.

At the simplest level, the transfer function of a multiplier may be written as:

Here V_OUT is the output voltage and the input voltages are V_INX and V_INY. The voltage V_REF must be present to ensure that the equation is dimensionally correct. In the multiplier CAM this voltage is set to be the internal reference voltage, nominally 3V.

We immediately see that the transfer function from the input V_INX to output V_OUT is controlled by the ratio V_INY/V_REF.

This is clearly a non-linear circuit because the transfer function V_INX to V_OUT is not fixed, it varies as V_INY varies.

Multiplication in 1, 2 and 4 quadrants

The output voltage of a multiplier may be sensitive to the polarity of neither, one or both of its inputs.
If the multiplier is sensitive to only one of the input voltage polarities then the transfer function may be written as:
Here the output voltage has a polarity which reflects that of V_INY but not that of V_INX.
When the multiplier is sensitive to both input polarities we have four quadrant multiplication.

Multiplier CAM Internals

A half-cycle offset compensated gain stage is used as the basic circuit element for the multiplier CAM.
The second input to the CAM is V_INY (shown as Y+ and Y- in Fig 6). This input is sampled by the ADC within the CAM.

The result at the ADC output is an eight-bit digital word D_OUT corresponding to the V_INY value.

For example, if V_INY were equal to +V_REF then D_OUT = 01111111.

To implement a multiplier, the digital word D_OUT is written to the appropriate RAM location such that it sets the value of the input capacitor for C1.

u is the unit capacitance.

One drawback of the circuit shown in Figure 6 is that the capacitance written as a representative value of V_INY can only ever have a positive value because there is no physical element to make a negative capacitance.

Accuracy Differences Between the Two Multiplier Inputs

The multiplier CAM has two inputs, V_INX and V_INY. The X input is fed directly into the gain stage, but the Y input is fed into the ADC.

Example Waveforms

These waveforms are produced with a sample and hold circuit on the output, so that the half-cycle nature of the output is removed.

Removing the sample and hold circuit from the output allows us to see the half-cycle nature of the output.

Figure 13 and 14 show more examples of multiplier operation.

Conclusions

The multiplier CAM has been described in terms of how it works, as well as its internal architecture. It has been shown that the two inputs have the same effect on the output voltage to a first order, but there are significant practical differences which the user must consider to extract maximum performance from the CAM.