© 2007, Kevan Hashemi Open Source Instruments Inc.

Here we define the terms RF, IF, LO, mixwer, attenuator, dBm, and dB. We explain the significance of 50 Ω in our circuits, and we provide a table that relates power in 50-Ω circuits like our to signal amplitude.

By RF we mean Radio Frequency, which is a signal with a frequency in the neighborhood of the frequencies we plan to transmit or receive through an antenna. In other words, the meaning of the term radio frequency is defined by our application. If we were designing an medium-wave receiver, our RF signals would be any signals of around 1 MHz. But we're not designing a medium-wave receiver. We're designing a 900-MHz ISM-band telemetric monitoring system. For us, radio-frequency means a signal with frequency in the neighborhood of 900 MHz.

By IF we mean Intermediate Frequency, and by LO we mean Local Oscillator. Both terms are used in the context of a circuit element called a mixer. We explain IF, LO, and mixers in detail elsewhere. In brief: a mixer multiplies a and input with a larger LO input to produce an IF output whose frequency is the difference between the RF and LO frequencies, and whose amplitude is proportional to the RF amplitude.

The mixer we use in our Demodulating Receiver (A3017) is the ADE-2ASK by Minicircuits. For our Stage Four experiments, we invested in a ZAD-11 mixer with BNC sockets on it. We put BNC sockets on all our circuits also, and we connected them together with BNC cables. This allowed us to switch circuit elements, plug them into mixers like the ZAD-11, and also BNC attenuators.

We can't get a good look at our RF signals directly. That's why we use mixers. The mixers shift the frequency of the signal we want to look at down to a frequency we can see on our 300-MHz oscilloscope. Having said that, our oscilloscope can see 900 MHz, it's just that the amplitude of 900 MHz is severely attenuated (by 17 dB, see here), and this attenuation changes rapidly with frequency (which we used to our advantage early on, see here).

Another thing we made use of in Stage Four is BNC-mounting fixed attenuators. A fixed attenuator reduces the power of an incoming signal by some fixed proportion on the way to the attenuator output. If you put a signal into a 3-dB attenuator, such as the HAT-3, it comes out half as powerful as it went in.

When we discuss RF signal power, which we do a great deal in the passages below, the power of a signal is the energy per second it transfers into its load. This load is invariably 50-Ω in our circuits. To our RF signals, coaxial cables look like 50-Ω loads, as do our amplifiers, filters, mixers, and attenuators. We try to make our printed circuit board traces act like 50-Ω loads. The cables and traces look like 50 Ω loads because of the way their intrinsic inductance and capacitance interact with the incoming RF signal (they are transmission lines). The other components look like 50-Ω loads because they are designed that way.

If one of our RF signals was to pass along a cable and hit a 500-Ω load, almost all of it would bounce off, like a wave hitting a wall, and return to its source. If it hits a 5-Ω load, the same thing happens, like a wave hitting a bridge that's just above the water level. Because we want our signals to propagate through our circuits, we make sure they see a 50-Ω load when they get to the end of every cable and trace. Not only that, we found that various amplifiers would be unsable if connected to non-50-Ω loads.

All our RF signals pass into 50-Ω loads, or as near as we can make them. When we talk of a 1-mW signal, we mean a signal that develops 1 mW in a 50-Ω load. That means it's root mean square amplitude is 224 mV, it's peak amplitude is 316 mV, and its peak-to-peak amplitude is 632 mV. Peak-to-peak voltage is the easiest thing we measure with an oscilloscope. But we convert peak-to-peak voltage to dBm, which is the most useful unit in our analysis.

Power Ampltude
1010 mW710 mV1 V2 V
01 mW220 mV320 mV630 mV
-10100 μW71 mV100 mV200 mV
-2010 μW22 mV32 mV63 mV
-301 μW7.1 mV10 mV20 mV
-40100 nW2.2 mV3.2 mV6.3 mV
-5010 nW710 μV1.0 mV2.0 mV
-601 nW220 μV320 μV630 μV
-70100 pW71 μV100 μV200 μV
-8010 pW22 μV32 μV63 μV
-901 pW7.1 μV10 μV20 μV
Table: Power in dBm and Watts, and Corresponding RMS Amplitude, Peak Amplitude, and Peak-to-Peak Amplitude.

By convention, we call a 1-mW signal one with power 0 dBm, where dBm is a logarithmic (decibel) measurement of power with respect to 1 mW. A 100-μW signal, being ten times less powerful, is −10 dBm. A 1-pW signal is −90 dBm. A change of 10 in dBm is a factor of ten change in power. An amplifier that multiplies the amplitude of a signal by 10 increases the signal power by a factor of 100. Instead of saying its gain is ×10, we say it's gain is +20 dB. A −30 dBm signal entering such an amplifier should emerge as a −15 dBm signal. Already you can see the benefit of working in dB and dBm: you get to add power units instead of multiply them.