# Power Gain and Loss Formulas to Determine Effects on Circuit Functionality

January 3, 2020 We, as humans, have an obsession with order, rankings, and the arbitrary positioning of things. From a psychological viewpoint, this allows us to quantify a perceived value or the level of importance of certain things that ordinarily defy such parametric analysis. This apparent obsession encompasses almost every aspect of our daily lives. We cannot help ourselves, because, at some point in your day, you will consciously or subconsciously rank some arbitrary person, place or thing.

Furthermore, this obsession goes beyond reason at times, but yet we still find a way to justify our thought process. Even in sports, whether it is collegiate or professional, we have our esteemed rankings systems. At the beginning of each season or week and the end of each season or week, we patiently (mostly) await the outcome of the rankings.

Furthermore, in my world of sports (the NFL), we have a power rankings system that depending on whether your team suffered a loss or won, they will gain in the power rankings or lose positional status. Although it is a relatively simple and straightforward approach, it is mostly meaningless, case in point, New England's loss to Baltimore. However, power gains and losses in the world of electronics is critical to overall design, functionality, and performance. Also, being able to calculate these values accurately is vital to circuit functionality and design; luckily, there is a formula for that.

## Defining Power and How it is Measured

Electrical power is the rate at which an electric circuit transfers electrical energy. Furthermore, the unit of measure for power is called watt (one joule per second). Electrical power, like mechanical power, is also defined as the rate of doing work, measured in watts, and is denoted by the letter P. In summary, you can think of power as the rate of energy consumed or supplied by an electric element over a measurable time. The formula for power is as follows:

P(power) = I(current) * E(voltage)

Moreover, in terms of an electronic circuit, the two primary parameters are voltage and current. However, assessing these two parameters (voltage and current) is not enough to sufficiently express electrical circuit behavior. Therefore, it is more beneficial in many cases to determine the amount of (electrical) power a particular circuit can handle to gauge circuit behavior accurately.

For example, we have all witnessed at some point, how a 75-watt bulb produces less measurable light than a 100-watt bulb. Also, regards to the electrical consumption of these bulbs, a cost is incurred.  When examining our utility bill more closely, you will notice that you are paying for an amount of power in use during a measurable (circuit behavior) amount of time. Thus, in essence, an electric power calculation is nothing more than an analysis of an electrical circuit network.

## How to Calculate Power Gain

We are all aware that when considering an electrical circuit or trace on a PCB, voltage, and current are always a consideration. However, when we are referring to an amplifier, for example, it is mostly about gain. Furthermore, not even this is so straightforward when we venture into the realm of high-frequency designs.

As I am sure you are aware, in a standard electrical circuit, the gain mostly involves voltage gain or Av. However, it can also, on the rare occasion, include current gain as well, but you do not require an amplifier for that. Besides, in a matching network, you can exchange current gain for voltage gain or vice versa. In summary, an amplifier’s primary feature is to provide power gain, not current or voltage isolation.

Therefore, being able to assess the power gain of an amplifier in your design scheme is imperative. There are a few parameters we must clarify first before we can fully understand what this power gain formula indeed assesses.

## Types of Defined Power Gains

Subsequently, you can define output as well as input power in different ways, and this also means that you can define power gain in alternative ways.

For example:

GP =: Here, GP represents operating power gain, PL stands for power delivered to load, and Pin stands for power delivered to the network.

GT =: Here, GT represents transducer gain, PL stands for power delivered to load, and Pavs stands for power available from the source.

GA =: Here, GA represents available gain, Pavn stands for power available from the network, and Pavs stands for power available from the source. From circuits to chips, power gain equations and loss formulas are necessary to know.

## What is Power Loss?

When referring to power, there are positives and negatives as in life, but they are called power gains (positive) and power losses (negative). A power loss in a power system, electrical circuit, or electronic circuit is due to a myriad of possible factors.

This dissipation of power is due to factors such as inductance, capacitance, and resistance. Other factors include undesired heating of resistive components, skin effect, losses due to cores and windings in transformers, and magnetic loss due to eddy currents. There can also be losses during electrical (power) transmission, hysteresis, dielectric loss, as well as various other factorial effects.

As I stated previously, an electronic circuit must compete with many factors in its attempt to remain efficient. However, loss of power with an electronic circuit or component is inevitable. Furthermore, mitigating these losses is vital, and the first step in undertaking this task is knowing how to calculate power loss.

## A look at Calculating Power Loss in a Circuit

Power loss in its purest form is power in minus the power out or PL = Pin - Pout. The rule for total power in comparison to individual power is that it is additive for all circuit configurations, whether it is parallel, series, or series/parallel. Also, as I am sure you remember, power is a measure of the rate of work, and since the power dissipated must equal the total power applied by the source(s) (Law of Conservation of Energy), then circuit configuration does not affect the mathematics.

Now, for example, we will use the diagram above. If you notice, the circuit utilizes a 9-volt source for its input, and a step-down voltage (linear regulator) of 5 V: our desired voltage. Also, our load on the 5-volt out has a maximum current of 1 ampere.

With these parameters in place, what will our power be in under these circumstances? Well, first of all, our regulator acts like a variable resistor that adjusts its resistance as required to maintain a constant 5-volt output. So, with our output at 1 ampere, we calculate power as P = I (1 A) * E (5 V), which means Power = 5 watts out.

Now compare this to the input, P = I (1 A) * E (9 V), which means Power = 9 watts for our input. This also means that we have a 4-volt drop across the regulator at 1 ampere. Using our formula for power and this equates to a dissipation (loss) of 4 watts (power). Finally, when we use the formula for power loss, PL = Pin – Pout, we get the result of PL = 9 watts – 5 watts or PL = 4watts. Testing the power of a circuit can be done long before producing the actual circuit.

Every designer is cognitive of the factors involving loss and gain in regards to power. This is in direct correlation with every designer's goal of peak efficiency. Overall, there is a critical need to understand the root causes of the factors that affect power gain and loss, and the need to be able to calculate them as well. Both are vital parts in the creation of accurate, functional, and high-performing circuit designs.

Implementing the use of power gain and loss formulas in PCB designs is easy with Cadence’s suite of design and analysis tools. Whether it’s through the variety of system analysis tools such as those found in Sigrity or utilizing the premiere layout functionality of Allegro your current and future PCB designs are assured to be profound.

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