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.
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 …
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.
- 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.
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.
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.
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.
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.
The component values can be selected as shown in Figure 7.
Figure 8 shows the whole circuit from my point of view.
We can determine the components required as shown in Figure 9.
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.
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.