## Introduction

I am always looking for real-world examples of analog computation and this blog post will discuss one of the best examples of analog computation that I found. I found this little gem in EDN magazines’ Design Ideas section, which is a great place to look for clever analog solutions for real problems.

The circuit that I am going to review here is shown in Figure 1. During my analysis, I will break the circuit down into sub-circuits and then analyze the sub-circuits.

Figure 1: EDN Circuit For Measuring Available Wind Power.

This circuit generates a voltage that is proportional to the wind power currently available. It does this using two sensors:

• anemometer/wind turbine

I usually think of four rotating cups whose motion generates a signal with a frequency proportional to wind speed, which is how this circuit represents wind speed.

• base-emitter junction of a transistor

The base emitter junction’s voltage variation with temperature provides an analog for the temperature variation of the air’s density.

This review needs to cover a lot of technical territory so let’s dig in …

## Background

For background on windmills and how they work, see this web site. The key equation for computing the maximum normalized power from a windmill is given by Equation 1. The normalized power is defined as the available watts per unit area of wind turbine.

 Eq. 1 $\displaystyle P=\frac{1}{2}\cdot A\cdot {{\rho }_{Air}}\cdot v_{_{Air}}^{3}\Rightarrow {P}'=\frac{P}{A}=\frac{1}{2}\cdot {{\rho }_{Air}}\cdot v_{_{Air}}^{3}$

where

• ρAir is the density of air, which is a function of temperature and pressure.
• vAir is the air velocity.
• A is the area of the wind turbine.
• P′ is the watts per unit area of the wind turbine.

Our objective in this post is to analyze the circuit shown in Figure 1 and demonstrate how that circuit implements Equation 1.

Before we do any electronics design, we need to beat Equation 1 into a form that can be implemented using electrical components. Figure 2 goes through this derivation.

Figure 2: Rework of Equation 1 into am Electronics-Friendly Form.

## Analysis

### Requirements

The circuit designer (Woodward) appears to have worked to the following requirements:

• The circuit is generate 1 V of output for every 1 kW/m2of available wind power per unit area.

The circuit can produce a wide range of values. A value needs to be chosen in order to determine concrete part values.

• The circuit is to use a single power supply voltage.

This circuit provides a nice illustration of designing an analog circuit for single supply operation. A one-supply design is normally preferred over a multi-supply design because it is cheaper. The designer used parts based on the 4000 series of CMOS devices. This is a very old family, nonetheless, many designers have a fondness for this family of digital parts for analog applications. See Appendix B for details on using these parts in analog applications.

• The anemometer measuring the wind speed generates a signal with a frequency variation of 10 Hz per 1 m/s of wind velocity.

The circuit can be adapted to various types of anemometers. We need to pick a specific conversion factor in order to pick specific components. Appendix C gives examples of anemometers that would work for this circuit.

• The circuit will compensate for air density variations with temperature.

It turns out that this compensation is relatively simple. Appendix A contains a derivation of the calibration equation presented in the designer’s original article.

For this analysis, I will break the circuit up into three sub-circuits:

• Forward-Biased Diode

The forward diode voltage drop will be shown to have a temperature variation very similar to that of air.

• Frequency-to-Voltage Conversion

This circuit will be used to multiply the forward diode voltage drop times the frequency of the signal from an anemometer.

• Level Shift and Amplify Stage

This circuit removes a DC bias and properly scales the output signal level.

### Forward-Biased Diode Voltage and the Density of Air

Figure 3 shows how the density variation for air on a percentage basis is similar to the percentage forward voltage variation across a diode or base-emitter junction.

Figure 3: Variation of Air Density with Temperature Compared to a Diode’s Variation.

Note that the molecular weight of air is 28.97 gm/mol, which is computed at this web site.

### Voltage-to-Frequency Converter Section Operation

Figure 4 summarizes how the frequency-to-voltage converter works.

Figure 4: Voltage to Frequency Converter Subsection Operation.

As shown in Figure 4, the frequency-to-voltage converter circuit generates an output with ripple on it. This ripple will be filtered out by the low-pass filter incorporated into the Level Shift and Amplify sub-circuit.

Figure 5 shows how I will represent the frequency-to-voltage converter as a circuit element.

Figure 5: Symbolic Representation of the Frequency-to-Voltage Converter.

The Ref pin shown in Figure 5 deserves some comment. It connects to the positive input pin of the operational amplifier. In a system with bipolar supplies, the Ref pin would be connected to ground. Because this is a single-power supply application, the Ref pin will be connected midway between ground and the supply voltage value. The single-supply setup will product a VOUT with a DC bias. This bias is removed by the Level Shift and Amplify stage.

### Level Shift and Amplify

Figure 6 shows the final stage of the circuit, which takes the output of the frequency-to-voltage converters and provides some amplification and removes the 2.5 V bias.

Figure 6: Output Circuit for Level Shift and Amplify Stage.

The component values can be selected as shown in Figure 7.

Figure 7: Component Selection for Output Circuit Stage.

### Entire Circuit

Figure 8 shows the whole circuit from my point of view.

Figure 8: Whole Circuit from a Block Diagram Viewpoint.

We can determine the components required as shown in Figure 9.

Figure 9: Check of Final Component Values.

## Conclusion

I went through this circuit in excruciating detail because I thought it does a nice job of illustrating the kind of interplay between physics and electronics that often occurs in analog sensor applications. Also, I have a circuit application that I am working on that will use a circuit related to this one and I wanted to review this work before I pressed on with my circuit.

## Appendix A: Derivation of Calibration Equation

The original article contains an equation that is useful for calibration. I derive his expression in Figure 10.

Figure 10: Derivation of Circuit Calibration Equation.

## Appendix B: Designing Linear Circuits with 4000 Series CMOS Parts

There are quite a few designers who still use 4000 series parts (in this case, 74HC4000 series). See this document for details on applying these digital parts in an analog application.

## Appendix C: Example of an Anemometer with 10 Hz per m/sec Output

I thought it was worthwhile showing some anemometers with 10 Hz per m/sec output. Both examples are powered.