**
**
With few exceptions, the Caller ID standards used though out the
world, specify signal levels in one of three different units. They are
Vrms, dBV, or dBm.

**
****Vrms:**

Vrms represents a voltage level computed as the root mean square (RMS)
of the signal being measured. To calculate a signal’s RMS voltage
level, it is mathematically squared, followed by averaging it over the
time interval of interest, and then finally taking the square root.
Effectively the resulting voltage level can be though of being
equivalent to a DC voltage delivering the same power into a resistive
load. In practical terms these are nice units since any good volt
meter displays its voltage readings in Vrms. Note that many hand held
DVM’s (Digital Volt Meters) do not measure "True" RMS and
will not return correct readings for the FSK and DTMF signals used in
Caller ID transmissions.

**
****dBV:**

A second common convention for voltage signal levels are the units
of dBV. These are quite simple to use as they represent a RMS voltage
level that is expressed as a base 10 logarithm relative to 1 Vrms. The
following two equations are used to convert from dBV’s to Vrms, and
back again.

convert
from Vrms to dBV

convert from dBV to Vrms

As an example:

1 Vrms = 0 dBV

0.1 Vrms = -20 dBV

0.01 Vrms = -40 dBV

0.001 Vrms = -60 dBV

Doubling the voltage level of a signal always results in a 6 dB
increase in the dBV value. Likewise, reducing the voltage in half
causes a 6 dB reduction in the dBV value. A convenient aspect in using
dBV units is that a wide range of voltage levels can be expressed with
simple numbers. For most of the signals related to Caller ID, the
range in voltage levels span from about -40 dBV to 0 dBV.

**
****dBm:**

While dBm is probably the most commonly used unit when dealing
with levels on a telephone line, they open themselves up to the most
confusion. As with dBV, the units of dBm are a logarithmic unit to
base 10. However, instead of being relative to 1 Vrms, they are
relative to 1 milliwatt of power. But before you can calculate the
power dissipated into a load, you need not just the voltage level
across it, but its impedance as well. If a load’s impedance changes
with frequency, like most telephones do, then computing a dBm level
across the load becomes a very difficult task. Fortunately, for
virtual all audio applications (including telephones), a common
reference impedance of 600 ohms is used. This is why some documents
specify "dBm_{(600)}" instead of just "dBm".

So for example, if an AC voltage of 1 Vrms is developed across a
600 ohm resistor, the signal level, in units of dBm, is calculated as
follows:

(a) ^{*1}

and:
(b) ^{*2}

so:

which can be reduced down to...

(c)

^{
*1 P is the power in Watts across the 600 ohms
*2 Vrms is the voltage measured across the 600 ohm
resistor
}

The last formula (c) looks very similar to the one used for
computing dBV’s. In fact they are identical except that for dBm, the
number 2.22 is added to the result. Well that’s pretty simple.
However what is the dBm value when measuring 1 Vrms across the tip and
ring leads of a telephone on-hook? It’s impedance is not even close
to 600 ohms. It would be possible to measure the telephone’s
impedance and use that value in formula (a) and (b) above. But the
telephone’s impedance will change with frequency. So if the
measurement is made at a different frequency the impedance is
different, meaning the dBm level is different.

Fortunately when dealing with Caller ID signals, the impedance of
the telephone is completely ignored, and the load impedance is always
assumed to be 600 ohms. This seems to make little sense as units of
dBm represent power levels, but without taking into account the
impedance, the power can not be calculated. Without fixing the load
impedance to constant value, the units of dBm would find little use in
Caller ID applications.

The result of the simplification is that when using dBm units,
simply ignore the signal’s power and treat it as a voltage value
that is 2.22 dB higher than its reading in dBV, as in equation (c)
above. However, it is important to remember that when dealing with dBm
levels across the tip and ring leads of a telephone, you must assume
that the telephone as an impedance of 600 ohms. This has some
significant implications which will be explored in the next article in
this series.

Note 1: Here’s some common conversions between
various level units.

1 Vrms = 0 dBV = 2.22 dBm

0 dBm = -2.22 dBV = 0.775 Vrms (a bit more than 1 Vpeak)

1 Vpeak = 0.707 Vrms = -3.0 dBV

1 Vp-p = 0.354 Vrms = -9.0 dBV

Note 2: The units of dBm are also used in RF (Radio
Frequency) applications. However, in these areas, the reference
impedance is not 600 ohms, but almost always 50 or 75 ohms.