Operational Amplifiers and Linear Integrated Circuits – Theory and Application (Fiore)

Variable Naming Convention

One item that often confuses students of almost any subject is nomenclature. It is important, then, that we decide upon a consistent naming convention at the outset. Throughout this text, we will be examining numerous circuits containing several passive and active components. We will be interested in a variety of parameters and signals. Although we will utilize the standard conventions, such as for critical frequency and for capacitive reactance, a great number of other possibilities exist. In order to keep confusion to a minimum, we will use the following conventions in our equations for naming devices and signals that haven’t been standardized.

The Decibel

Most people are familiar with the term “decibel” in reference to sound pressure. It’s not uncommon to hear someone say something such as “It was 110 decibels at the concert last night, and my ears are still ringing.” This popular use is somewhat inaccurate, but does show that decibels indicate some sort of quantity – in this case, sound pressure level.

Decibel Representation of Power and Voltage Gains

In its simplest form, the decibel is used to measure some sort of gain, such as power or voltage gain. Unlike the ordinary gain measurements that you may be familiar with, the decibel form is logarithmic. Because of this, it can be very useful for showing ratios of change, as well as absolute change. The base unit is the Bel. To convert an ordinary gain to its Bel counterpart, just take the common log (base 10) of the gain. In Equation form:

Note that on most hand calculators common log is denoted as “ ” while the natural log is given as “ ”. Unfortunately, some programming languages use “ ” to indicate natural log and “ ” for common log. More than one student has been bitten by this bug, so be forewarned! As an example, if a circuit produces an output power of 200 milliwatts for an input of 10 milliwatts, we would normally say that it has a power gain of:

For the Bel version, just take the log of this result.

If you look carefully, you will notice that a doubling is represented by an increase of approximately 3 dB. A factor of 4 is in essence, two doublings. Therefore, it is equivalent to 3 dB + 3 dB, or 6 dB. Remember, because we are using logs, multiplication turns into simple addition. In a similar manner, a halving is represented by approximately -3 dB. The negative sign indicates a reduction. To simplify things a bit, think of factors of 2 as 3 dB, the sign indicating whether you are increasing (multiplying), or decreasing (dividing). As you can see, factors of 10 work out to a very convenient 10 dB. By remembering these two factors, you can often estimate a dB conversion without the use of your calculator. For instance, we could rework our initial conversion problem as follows:

• The amplifier has a gain of 20
• 20 can be written as 2 times 10
• The factor of 2 is 3 dB, the factor of 10 is 10 dB
• The answer must be 3 dB + 10 dB, or 13 dB
• This verifies our earlier result