## 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.

## Measure a Bipolar Signal with an Arduino Board

Arduino is a popular family of open source microcontroller boards. Hobbyists, students and engineers all over the world use this platform to quickly design and prototype a microcontroller driven circuit. One of its interfaces with the analog world is the ADC. Since these boards are mostly designed around an ATMEL ATmega32 or ATmega168 microcontroller, the ADC has 8 inputs and 10-bit resolution, making it suitable for many applications.

From time to time I receive a message through my Contact page with the question, how to interface a sensor, or an outside circuit with the Arduino ADC? In most cases the answer is an interface between a bipolar circuit and the Arduino board. As the bipolar circuit output varies from some negative to a positive level, the Arduino ADC cannot measure this signal directly, because the ADC inputs can only be between 0V and the reference voltage.

In one of these messages a reader asked me how to build an interface between a board that has an output voltage of -2.5V to +2.5V and the Arduino ADC. He told me that the Arduino reference voltage is AVCC = 5V. He would like to measure the +/-2.5V signal with the Arduino board and direct the microcontroller to take some action based on the result.

## Measure a Wheatstone Bridge Sensor Signal with an ADC

I received a message from one of my readers asking me to help with a Wheatstone bridge circuit. Since my response to him bounced back, and this being an interesting subject, I decided to write this article. Here is what he writes:

I found a circuit to condition the output of the Wheatstone bridge in the National ADC1205 datasheet, page 16. It uses an Op Amp configured as follows: V1 from the bridge thru 10K resistor to (–) input of Op Amp, 1.5Meg feedback resistor and Vout connects to the V- of the 5V ADC. V2 from the bridge connects directly to (+) input of the op amp and the V+ of the ADC.

The bridge V2-V1 is 0 mV to 30 mV. This is both at 5.000 V (0 mV) and V1 = 4.985 V, V2 = 5.015 V (30 mV). Please advise the equations to calculate how this works. Since the ADC is 5 V, I cannot see how the Vout can exceed that voltage. Is it true that Vout = 5.015 V when V1 = V2 = 5.015 V and ADC Out = 0 V?

The National ADC1205 is an obsolete component now, but the advice and application notes are still valid. We can use any ADC if we can correctly adjust Vref and the operating conditions. We can use an Arduino board as well, with its 10-bit ADC to achieve a complete system.

## Apply Thevenin’s Theorem to Solve a Negative Resistance Circuit, or Current Source

The circuit in Figure 1 is a good example of applying Thevenin’s Theorem to solve a circuit with dependent supplies. It is a negative resistance circuit and it was posted in this forum with a call for solution verification for IL as a function of Vin. With some clever resistor values, the circuit can also be a current source with RL its load. Since this fits very well with my plans to write more about Thevenin’s Theorem, I decided to post the solution here.

Figure 1

## Using the Summing Amplifier as an Average Amplifier

Sometimes people ask how can one use a summing amplifier as an average amplifier. The answer is simple, provided that one knows what kind of average one needs.

The summing amplifier can output the average of two, three or more signals. This is different than a signal average. The summing amplifier cannot, for example, output the average of a triangle signal. For that, you need an integrator to perform the average in the analog realm, or you need to sample the signal and calculate the average with a microcontroller. This type of average is the signal average in the time domain. I will write an article about the average of a signal in a near future.

In this post I will show you how to average two or more signals with a summing amplifier. In How to Derive the Summing Amplifier Transfer Function I wrote that the summing amplifier shown in Figure 1

## How to Design a Circuit from its Transfer Function Graph

Sometimes all we know about a circuit is its transfer function graph.   The transfer function might look like the one in Figure 1.  How can we design a circuit so that its input-output behavior will match the graph?

Figure 1

The design starts with the mathematical form of the transfer function.  This is a linear function, with the general form of a first order polynomial function.