## The Basics

What is a Bridge Rectifier?

A bridge rectifier (BR) is a type of circuit component made up of 4 diodes that causes an AC input to change to a DC output. Because of its design, it can output full wave rectification, meaning that all of the alternating input can be flipped over the x axis, making everything positive or a direct output. This allows for BRs to be more efficient as they are able to capture more of the input signal by creating a full wave rectification.

Animation demonstrating how a Bridge Rectifier Works [1]

When a capacitor is added to a BR circuit, similar to that of an RC circuit, instead of acting as a filter with lower frequencies, the capacitor in a BR circuit smooths out the voltage as this allows for a more steady and practical output to a power supply [2]. This also improves the average DC output through connecting capacitors in parallel with a load, as the capacitor acts like a storage device and can then discharge onto the connected load.

BR Circuit with Capacitance and Resultant Waveform [2]

When sizing the capacitor and resistor for the circuit, it will be optimal to use both high capacitance and resistance, as the higher capacitance will allow for a higher voltage, therefore more power going to your battery load, and a higher resistance will be used for safety as to allow a place for surge current to go if the capacitor is at its maximum. This concept is further explained below under experimentations.

## Circuit Experiments

Multiple Bridge Rectifier circuit experiments were conducted to analyze how the values of resistance and capacitance, as well as how they interacted in parallel with the rectifier, impacted the output voltage over the capacitor and influenced discharge time.

To conduct the experiments, a Moku Go was used to induct a frequency across the system. To learn how to set-up your own Moku Go, see the following videos we used to get started and learn how to use the oscilloscope feature:

For our Bridger Rectifier circuit experiments, we used a breadboard, 4 1N4007 diodes, a variable resistor box, a variable capacitance box, and the Moku Go with alligator/banana clips and oscilloscope probes to send a signal through the circuit and read the output voltage over the capacitor.

A picture of our circuit set-ups with a load and without a load and attached to the Moku Go are shown below.

BR Circuit Set-Up with Load/Resistor Box

BR Circuit Set-Up without Load/Resistor Box

If you want to see another way of learning how to set up this circuit, see this Instructables page: https://www.instructables.com/Make-A-Bridge-Rectifier-From-Diodes/

Our first experiment was to identify how the output voltage would change based on a changing capacitance value while holding a resistance (load) value constant. For this experiment, a resistance of 570 Ohms was chosen and a capacitance value ranging from 0.47 uF to 47 uF was run through and analyzed over a time interval. A graph overlaying five different trials is shown below.

BR Circuit with resistance of 570 Ohms and varying capacitance from 0.47uF to 47uF

As shown, as the capacitance increases, the output voltage smooths out more, meaning that the rate at which the capacitor is discharging decreases compared to values of lower capacitance. When the capacitor has a smaller rating, the voltage drop is quicker when the input square wave turns off compared to that of the capacitors with a higher rating. Because our final circuit will want a smoother output voltage, we will want to look into using higher capacitance. In addition, further experimentation is needed to analyze the discharge rate of these different capacitances.

To expand upon our first experiment, we ran time-based experiments of the Bridge Rectifier circuit using a constant resistance (load) value and varying capacitance. We wanted to see how a capacitor would discharge through different loads attached in parallel, similar to how a battery will in the future of our project. We used a 5uF capacitor and our resistance ranged from 10kOhms to 5MOhms. Shown below is the point as which the square wave input signal (5V or 60Hz) was turned off and the capacitors discharged through their respective load amount.

Discharging curves for a 5uF capacitor over different resistance values

As the resistance (load), increased, the time it look for the capacitor to fully discharge increased, shown by the yellow line on the graph. When a load and capacitor are in parallel, the current traveling through the circuit wants to take the path of “least resistance.” So when you increase your resistance or load for the current stored on the capacitor to dissipate through, it will want to stay on the capacitor longer as compared to moving through the load/resistor.

Our next experiment involved running the same input frequency/voltage through only a capacitor and letting it dissipate by itself, with no load attached in parallel in the circuit. This could allow us to see how just the capacitance affects the voltage discharge rate. Five different capacitance values were tested, doubling in value each time, and the results are shown below.

Analyzing Voltage & Discharge Rate over Changing Capacitance

As shown above, as the capacitance increases, the time it takes for the capacitor to fully discharges increases. This discharge rate is important for when we are sizing our batteries for our full system. Because we will have fluctuation in our input from waves, it will be important to use a higher capacitance in our ESS because they have a longer discharge time. This will be needed as when the input waves are not at their peak for the system, a higher capacitance will allow for a steady discharge of current into the batteries for a longer period of time as compared to a smaller capacitance value discharging quicker, and therefore not being as efficient. Overall, a higher capacitance will allow for the rate to be steady and consistent in order to match the battery rating and to increase the longevity of the battery.

We conducted another experiment comparing voltage drops over both the capacitor and resistance (load resistance within a battery) at the same time to see how that might affect filtering, overall voltage, and the discharge rate. Once again, 5 Vpp and 60 Hz was the input and the results are compiled below.

Comparing Voltage & Discharge Rate over Varying Capacitance & Resistance

As shown above, a similar trend occurs with the voltage and discharge rate as both the capacitance and resistance values are increased. Like in the individual experiments, increasing the capacitance increases the discharge rate and increasing the resistance also increases the discharge rate and output voltage starting value. A great example is to comparing the green and red resistance change from 10kOhms to 100kOhms with the same capacitance. As shown, the lower resistance (green curve) discharges quicker in comparison to the higher resistance, while the higher resistance is capturing a higher output voltage.

In order to identify the best resistance within the battery, this relationship will need to be explored between load resistance and capacitance further with available batteries on the market in order to most efficiently size components of the ESS.

Using these experiments, we were able to draw conclusions that our capacitance component should have as high of a capacitance as we can create within our lab’s constraints. In addition, further testing and research is needed to determine how resistance should play a part within the circuit in order to help with filtering but not decrease total power output.

## References

[1] “How a Bridge Rectifier Works.” Electronics Gurukulam. [Online]. Available: https://electronicsgurukulam.blogspot.com/2012/04/how-bridge-rectifier-works.html

[2] “Diode Clippers.” Electronics Tutorials. [Online]. Available: https://www.electronics-tutorials.ws/diode/diode_6.html