I recently read an article in a well-known consumer-facing technical hobby magazine, where the author used the phrase, “watts per day.”Ā This is an erroneous concept (the technically-trained author should have known better), which illustrates a matter that is often confusing to the average person.

“Watts per day” is not a meaningful unit of measurement.

The watt (W) is a unit of power, which is defined as the rate at which energy is transferred or used. One watt is equal to one joule per second (J/s).

The unit of energy is typically measured in joules (J), but it is also commonly measured in watt-hours (Wh) or kilowatt-hours (kWh). One watt-hour is equal to one watt of power used for one hour, and one kilowatt-hour is equal to one kilowatt (1000 watts) of power used for one hour.

In other words, the “watt” conveys the notion of the rate of energy consumption. When we pay for energy consumed, we pay for kilowatt-hours.

Therefore, if you see the phrase “watts per day,” it is likely that the author was trying to convey the notion of power used over a period of one day, and the correct usage would be to express it in terms of watt-hours (or kilowatt-hours) per day.

As an example: if a piece of equipment is rated at 100 watts, and the equipment is used for 8 hours every day, then we can say that the equipment consumes 800 watt-hours of energy (not power) per day.

The WNET Group has announced plans to launch NEXTGEN TV service in New York City and surrounding areas – the #1 television market in the country encompassing approximately 7.45 million TV households.

AGC Systems is one of the key organizations supporting The WNET Group with extensive engineering testing and operational planning based on the ATSC 3.0 suite of NextGenTV technologies.

Neal Shapiro, President & CEO of The WNET Group, expects that this transition “will modernize the New York City broadcast market infrastructure to deliver high-quality broadcasts with the latest technology available.”

The FĆ³rum Sistema Brasileiro TV Digital Terrestre (SBTVD Forum) has recommended to the Brazilian government the selection of several technologies proposed by ATSC for Brazilās next-generation terrestrial digital television standard.Ā AGC Systems has been actively involved in the proposal and testing process, on behalf of several clients, resulting in adoption of the SL-HDR1 High Dynamic Range system and MPEG-H Audio coding.

ATSC President Madeleine Noland congratulated the ATSC IT-4 Brazil Implementation Team, of which AGC Systems’ Aldo Cugnini is a member. āIT-4 members have been diligently supporting ATSC technologies throughout the process and will continue their efforts in the upcoming phases of the SBTVD evaluation process.ā

The SBTVD development of āTV 3.0ā specifications and additional testing will continue over the course of the next two years.

Philips has now been at the forefront of technology for 130 years. AGC Systems President Aldo Cugnini is proud to have Philips as a key client and past employer.

PROCLAMATION OF STATE OF EMERGENCY TO ALL CITIZENS AND PERSONS WITHIN THE TOWNSHIP OF WASHINGTON AND TO ALL DEPARTMENTS, DIVISIONS AND BUREAUS OF THE MUNICIPAL GOVERNMENT OF THE TOWNSHIP OF WASHINGTON:

WHEREAS, pursuant to the powers vested in me by Chapter 251 of the laws of 1942, as amended and supplemented, N.J.S.A. App. A:9-30 et. seq.; N.J.S.A. 40:48-1 (6), and ordinances enacted pursuant thereto; N.J.S.A. 2C:33-1 et. seq., Executive Order 103 and by ordinances adopted by the Township of Washington I have declared that a STATE OF EMERGENCY exists within the Township of Washington; and

WHEREAS, the aforesaid laws authorize the promulgation of such orders, rules, and regulations as are necessary to meet the various problems which have or may be presented by such an emergency; and

WHEREAS, by reason of the rapidly evolving outbreak of the novel coronavirus, COVID-19, the need for government operations to address staffing capabilities to ensure essential operational needs are met in order to mitigate factors which may further adversely affect the health, safety, and welfare of the people of the Township of Washington and exacerbate and worsen existing conditions; and

WHEREAS, pursuant to N.J.S.A App. A:9-33.1, entitled “Emergency Powers of Government,” a disaster is defined as an unusual incident resulting from natural or unnatural causes which endangers the health or safety of residents; and

WHEREAS, it has been determined that in the event these areas of the Township of Washington should be declared disaster areas, and further that certain measures must be taken to ensure that the authorities will be unhampered in their efforts to maintain law and order as well as an orderly flow of traffic and further in order to protect the persons and property of the residents affected by the conditions and finally that governmental operations including but not limited to the conduct of public meetings shall be substantially altered; and

WHEREAS, all lands within the boundaries of the Township of Washington, as a result of the outbreak of the novel coronavirus, are hereby designated as disaster areas, in accordance with the “Emergency Powers of Government.”

NOW, THEREFORE, IN ACCORDANCE WITH the aforesaid laws, we do hereby promulgate and declare the following regulations shall be in addition to all other laws of the State of New Jersey and the Township of Washington.

/signed/

Matt Lopez, OEM Coordinator Township of Washington

US and Canadian broadcast experts met in Toronto this month, atĀ theĀ Barrett Centre for Technology Innovation, to discuss how the new ATSC-3 Broadcast standard provides new opportunities for mass distribution of content, information, and data.Ā Among the participants was AGC Systems’ Aldo Cugnini, who met with Humber College research staff, who are hoping to create and lead the way for Canadaās first “ATSC Living Lab.”

Math can be truly awe-inspiring, as in this example of the unexpected places that Ļ can show up. The proof is nothing short of elegant ā be sure to watch parts 2 and 3.Ā Astonishing!

This is one of my engineering pet peeves — I keep running into students and (false) advertisements that describe a power output in “RMS watts.”Ā The fact is, such a construct, while mathematically possible, has no meaning or relevance in engineering.Ā Power is measured in watts, and while the concepts of average and peak watts is tenable, “RMS power” is a fallacy.Ā Here’s why.

The power dissipated by a resistive load is equal to the square of the voltage across the load, divided by the resistance of the load.Ā Mathematically, this is expressed as [Eq.1]:

\large P=\frac{V^{2}}{R}

where P is the power in watts, V is the voltage in volts, and RĀ is the resistance in ohms.Ā When we have a DC signal, calculating the power in the load is straightforward.Ā The complication arises when we have a time-varying signal, such as an alternating current (AC), e.g, an audio signal or an RF signal.Ā Ā In the case of power, the most elementary time-varying function involved is the sine function.

In Figure 1, the dotted line (green) trace is our 1-volt (peak) sinusoid. (The horizontal axis is in degrees.) The square of this function (the power as a function of time) is the dark blue trace, which is essentially a “raised cosine” function.Ā Since the square is always a positive number, we see that the instantaneous power as a function of time rises and falls as a sinusoid, at twice the frequency of the original voltage.Ā This function itself has relatively little use in most applications.

Another quantity is the peak power, which is simply Equation 1 above, where V is taken to be the peak value of the sinusoid, in this case, 1.Ā This is alsoĀ known as peak instantaneous power (not to be confused with peak envelope power, or PEP).Ā The peak instantaneous power is useful to understand certain limitations of electronic devices, and is expressed as follows:

\large P_{pk}=\frac{V^{2}_{pk}}{R}

A more useful quantity is the average power, which will provide the equivalent heating factor in a resistive device.Ā This is calculated by taking the mean (i.e., the average) of the square of the voltage signal, divided by the resistance. Since the sinusoidal power function is symmetric about its vertical midpoint, simple inspection (see Figure 1 again) tells us that the mean value is equal to one-half of the peak power [Eq.2]:

which in this case is equal to 0.5.Ā We can see this in Figure 1, whereĀ the average of the blue trace is the dashed red trace.Ā Thus, our example of a one-volt-peak sinusoid across a one-ohm resistor will result in an average power of 0.5 watts.

Now the concept of “RMS” comes in, which stands for “root-mean-square,” i.e., the square-root of the mean of the square of a function.Ā The purpose of RMS is to present a particular statistical property of that function.Ā In our case, we want to associate a “constant” value with a time-varying function, one that provides a way of describing the “DC-equivalent heating factor” of a sinusoidal signal.

Taking the square-root ofĀ V^{2}_{pk}/2_{Ā }therefore provides us withĀ the root-mean-square voltage (not power) across the resistor; in this example, that means that the 1-volt (peak) sinusoid has an RMS voltage of

Note the RMS voltage is used to calculate the average power. As a rule, then, we can calculate the RMS voltage of a sinusoid this way:

\large V_{rms} \approx 0.7071 \cdot V_{pk}

Graphically, we can see this in Figure 2:

The astute observer will note that 0.7071 is the value of sinĀ 45Ā° to four places. This is not a coincidence, but we leave it to the reader to figure out why.Ā Note that for more complex signals, the 0.7071 factor no longer holds.Ā A triangle wave, for example, yields V_{rms} ā 0.5774 Ā·Ā V_{pkĀ }, where 0.5774 is the value of tanĀ 30Ā° to four places.

For those familiar with calculus, the root-mean-square of an arbitrary function is defined as:

Replacing f(t) with sin(t) (or an appropriate function for a triangle wave) will produce the numerical results we derived above.

For more information on the root-mean-square concept, see the Wikipedia articles Root mean square and Audio power.

Additional thoughts on root-mean-square

Because of the squaring function, one may get the sense that RMS is only relevant for functions that go positive and negative, but this is not true.

RMS can be applied to any set of distributed values, including only-positive ones. Take, for example, the RMS of a rectified (absolute value of a) sine wave. As before, V_{rms}=.7071 Ā· V_{pkĀ }, i.e., the RMS is the same as for the full-wave case. However, V_{avg}Ā ā 0.6366 Ā·Ā V_{pk} for the rectified wave (but equals zero for the full-wave, of course; 0.6366 is the value of 2/Ļ to four places). So, we can take the RMS of a positive-only function, and it can be different than the average of that function.

The general purpose of the RMS function is to calculate a statistical property of a set of data (such as a time-varying signal). So the application is not just to positive-going data, but to any data that varies over the set.