From: "nanchez" on Fri 3 Jun 2005 14:59

I'm doing some RF experimentation and I need to know the "relation"
between dBm specificatons and voltage level for a signal.

I have a RF mixer with a specification that says:

LO drive level (50 ohm) = -16 dBm

And I have a LO source that give me an output of 2.5Vpp to a capacitive
load of 5pF at 40MHz.

How can I relate both items and design a circuit to connect LO source
to RF mixer ?

A basic definition that is industry-wide, government-wide,
has "dbm" as decibels at "0 dbm" related to a power level of
1.0 milliWatts in a "50 Ohm system." That has become so
widespread that specification writers don't always include
those words. It is implicit when referring to RF components.

The RMS voltage can be quickly calculated from some identities
on the basic formula for Watts: P = E x I. Knowing R (50 Ohms)
one can substitute Ohm's Law of Resistance of I = E / R into
that to get E = SquareRoot (P x R).

For 1.0 mW in a 50 Ohm system, P x R = 0.050 and the square
root of that is 0.2236 so 0 dbm has an RMS voltage of 223.6
milliVolts.

In your mixer specification, -16 dbm is equal to 35.44 mV
RMS across a resistance of 50 Ohms.

You can't DIRECTLY use your 40 MHz source value of 2.5 V
peak-peak across a 5.0 pFd capacitance because it does not
include the characteristic RESISTIVE impedance of 50 Ohms.
Power in Watts must be related to the impedance of a load
in order to perform "work." [a basic definition of power
in Watts is "a unit of work"]

Capacitance across a load will vary its impedance depending
on the frequency. For that reason the electronics industry
has long relied on a basic resistive impedance to measure
and characterize RF components. The result is the very
common "dbm" referred to 1.0 mW across a resistive 50 Ohm
load...or the characteristic impedance of the measurement
system, both source and load impedance.

To relate your mixer specification to your RF source, you
will have to put a 50 Ohm load across the source and
measure that. If you have some stray capacitance across
that load (inevitable) and know approximately what that is,
you can calculate its effect across a resistance. At 40 MHz
a 5.0 pFd capacitance has a reactance of 796 Ohms. That is
not much but it changes the magnitude of the parallel R-C
from 50.0 Ohms resistive to 47.0 Ohms slightly capacitive.
That's a small change and can generally be neglected for
experimental bench work.

If you have some web source to study about this items, I'll be glad to
hear about it.

It's in practically every textbook on the subject of RF
electronics. What can confuse newcomers to RF is the
implicit "standard" which is not always included in
specification sheets. The definition of "dbm" is arbitrary
and probably picked (way back in time) for sake of
convenience in measurement by all concerned.

The reason for picking "50 Ohms" in a "system" is more
obscure and ties into the physics of power transfer in
coaxial cables. That's a curiosity that some can look up
if they are interested but does not apply to how to USE the
"dbm" specifications. To use "dbm" one only needs to
remember the definition and apply simple forumulas for Power
and Ohm's Law of Resistance.

I hope that was of some help to you.