Design a Unipolar to Bipolar Converter the Easy Way with Microsoft Mathematics

Many analog circuits can be calculated with simple algebra. This may involve an equation or a system of equations, but the calculations are quite simple. Take the differential amplifier, as an example. In a previous article, MasteringElectronicsDesign: Design a Differential Amplifier the Easy Way with Mathcad, I showed how to design the differential amplifier by solving a system of two equations with two unknowns using Mathcad. Since then, readers asked me if there is any other substitute for Mathcad that they can use to solve the system of equations. And the answer is, yes, there is one.

Microsoft Mathematics is a free application which is loaded with features. Besides its graphing, math formulas and units converter, it has an equation solver that can easily handle systems of equations. By changing a few values and letting the application calculate the unknowns, a user can tweak his circuit to match the design requirements.

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How to Derive the RMS Value of Pulse and Square Waveforms

The RMS value of a pulse waveform can be easily calculated starting with the RMS definition. The pulse waveform is shown in Figure 1. The ratio t1/T is the pulse signal duty-cycle. As shown in other articles in this website (MasteringElectronicsDesign.com:How to Derive the RMS Value of a Trapezoidal Waveform and MasteringElectronicsDesign.com:How to Derive the RMS Value of a Triangle Waveform), the RMS definition is an integral over the signal period as in equation (1).

pulse signalFigure 1

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How to Derive the RMS Value of a Triangle Waveform

What is the RMS value of a periodic signal?  When a periodic signal is generated by a source connected to a load, a resistor for example, the RMS value is the continuous signal, the DC value which would deliver the same power to the load as the periodic signal.

This article shows how to derive the RMS value of triangle waveforms with different shapes and duty cycles.

The triangle waveform in Figure 1 has a slower rise time than the fall time.  In this case, the fall time is small so that it can be considered zero.  If it is not zero, read further on deriving the RMS value of a triangle with comparable rise and fall times.

triangle waveform with slow rise time, sharp fall timeFigure 1

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Differential Amplifier Calculator

Unipolar to Bipolar Converter Example

If you need to design a differential amplifier, here is a handy calculator. All you need to define are the input range, the output range and a choice of voltage reference.

The differential amplifier was explained in different articles on this website. Solving the Differential Amplifier – Part 1, Part 2 and Part 3 shows a numerical example and how to design such an amplifier. Also, the common mode voltage level and the common mode output error were explained in the series of articles The Differential Amplifier Common-Mode Error – Part 1 and Part 2.

Enter the input range, Vin1 to Vin2, the output range, Vout1 to Vout2 and a reference voltage Vref. You need to choose two resistors, R2 and R3. The calculator will compute R1 and R4.

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Design a Bipolar to Unipolar Converter with a 3-input Summing Amplifier

Since the publication of Design a Bipolar to Unipolar Converter to Drive an ADC, several readers contacted me with requests to help in solving their particular converter. The common problem they had was the fact that the components’ calculation resulted in a negative value for at least one resistor.

To provide a solution, first we need to understand the root cause of the problem. Let’s take one of the circuits I received and analyze it.

The reader wrote that he would like to drive an ADC with the input range of 0 to 2.5V from a signal with the range of –5V to +5V, connected at V1 (see Figure 1).

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Summing Amplifier Calculator

Bipolar to Unipolar Converter Example

The calculator solves the summing amplifier resistors based on the input and output voltage range requirements. It is a great tool to design a bipolar to unipolar converter, as an example and other circuits.

Enter the input range, Vin1 to Vin2, the output range, Vout1 to Vout2 and a reference voltage Vref which helps in adjusting the common-mode level of the amplifier. Since the 2-input summing amplifier has 4 resistors, you need to choose two resistors, R1 and R3, and calculate R2 and R4. For more details about this calculator read How to Design a Summing Amplifier Calculator.

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How to Design a Summing Amplifier Calculator

Several articles in this website describe the Summing Amplifier.  In one of these articles, Solving the Summing Amplifier, I showed a numeric method to design a non-inverting summing amplifier based on its input and output voltage range requirements.

This article shows how to design a summing amplifier calculator and the mathematical relations it uses.  You can find the calculator here:

JavaScript Summing Amplifier Calculator

Type the input voltage range, output range, a reference voltage and a choice of two resistors.  The calculator gives you the answer for the remaining two resistors.  The default values are for a bipolar to unipolar converter, which is explained in Design a Bipolar to Unipolar Converter to Drive an ADC.

What are the underlying equations?

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