## 1.1 What is Power?

Intro

What is Power? A discussion of the physical definition of power, and the electrical concepts of volts, amps, and watts. This leads to how the measurement of AC and RF power is complicated by complex impedance and phase shift.

Why do we want to measure Power? There are many reasons to measure RF power, spanning a wide range of industries and technologies. This subsection discusses the common uses of power measurement instruments, and the rationale.

A brief history of RF power measurements:

Power measurement has evolved considerably since the earliest days of wireless. Some of this history can be traced to well-known radio pioneers, and much of the innovation took place among companies still involved in the measurement industry. Berkeley Nucleonics and the technical community it has served for over 60 years are still very involved in this area of work.

Power Measurement Technologies:

A discussion of the key methods in use today for measuring RF power, including Thermal, Diode, Receiver-based, Direct RF Sampling, and Monolithic (IC) solutions.

CW versus Peak Power:

Power measurement has come a long way since early methods, which only produced meaningful measurements for unmodulated signals. This section focuses on the limitations of various types of power meters when measuring modulated signals, and how modern solutions have improved the situation.

Bandwidth and Dynamic Range Issues:

Not every signal aligns neatly with the capabilities of power measurement instruments. By understanding the bandwidth and dynamic range characteristics of your signal, it becomes easier to select the best measurement technology.

#### 1.1 What is Power?

In physics terms, power is the transfer rate of energy per unit time. Just as energy has many different forms (kinetic, potential, heat, electrical, chemical), so does power. One mechanical definition of energy is force multiplied by distance – the force moving an object multiplied by the distance it is moved.

Energy = Force x Distance

To get the power, or transfer rate of that energy, we divide that energy by the length of time to perform the move. Since distance per unit time is velocity, mechanical power is often computed as force times velocity.

Power = Force x Distance / Time

= Force x Velocity

In electrical terms, force equates to voltage, also known as Electromotive Force (EMF). This describes how much “pressure” the electrons are under to move. The velocity is analogous to electrical current, which is the charge (number of electrons) per unit time.

Power(electrical) = EMF x Current

EMF is typically measured in volts, and current is typically measured in amperes, or amps. One ampere is one coulomb (a unit of charge, equal to 6.2 x 1018 electrons) per second. Multiplying current and voltage together yields the power in watts.

Watts = Volts x Amps

In the case of steady voltage or steady current flow, computing the average power is simple:

– Simply multiply average volts by average amps. However, if both values fluctuate, as will be the case with alternating current, or AC, the average power can only be computed by performing a mathematical average of the instantaneous power over one or more full signal periods.

Limiting our discussion only to sinusoidal, AC waveforms, we can see that the power will fluctuate in synchronization with the voltage and current. For resistive loads, the current and voltage will be in-phase. That is both will be positive at the same time, and both negative. Analyzing graphically, one can see that either case produces positive power, since multiplying two negative numbers yields a positive result. See Fig. 1.1.1*

If there is a phase shift between current and voltage, there will be times that the voltage and current are of opposite polarities, resulting in a negative power flow. This has the effect of reducing the average power, even though the magnitude of the voltage and current has not changed.

For this reason, it is not generally sufficient to simply measure the voltage or current to characterize a signal’s power. A direct power measurement is best, in which the signal is applied to a precision termination (load), which keeps the voltage and current very close to in-phase. If this is done properly, a voltage measurement across the load can be performed to yield a meaningful power value, or the dissipated power can be computed directly by measuring the heating effect of the signal upon the load. This is discussed in great detail in the next section.