{"id":4970,"date":"2023-08-18T02:40:56","date_gmt":"2023-08-18T10:40:56","guid":{"rendered":"https:\/\/wonghoi.humgar.com\/blog\/?p=4970"},"modified":"2025-04-13T22:14:35","modified_gmt":"2025-04-14T06:14:35","slug":"navigating-between-oscilloscope-land-volts-and-rf-land-dbm","status":"publish","type":"post","link":"https:\/\/wonghoi.humgar.com\/blog\/2023\/08\/18\/navigating-between-oscilloscope-land-volts-and-rf-land-dbm\/","title":{"rendered":"Navigating between oscilloscope-land (Volts) and RF-land (dBm)"},"content":{"rendered":"\n

Have you ever been annonyed by the dBm and V units when you try to measure output from your benchtop signal generator (or arbitrary waveform generator, or ARB) with a spectrum analyzer, or measure a RF signal (sine) generator with an oscilloscope?<\/p>\n\n\n\n

TLDR<\/h2>\n\n\n\n

For \"50\Omega\" systems only. The fastest way is to work with squared<\/strong> voltages in linear scale with the provided ‘magic’ scaling factor (10 for amplitude and 20 for rms) and not mess with factorization in the log (dB) or anti-log (\"10^{\frac{\mathrm{dB}}{10}}\") process:<\/p>\n\n\n\n

P[\\mathrm{mW}]=2.5V_{pp}^2 = 10V^2=20V_{rms}^2<\/pre><\/div>\n\n\n\n
\\mathrm{dBmW}=\\mathrm{dB}\\left(10V^2\\right)=\\mathrm{dB}\\left(20V_{rms}^2\\right)<\/pre><\/div>\n\n\n\n
\\mathrm{dBmW}\\approx\\mathrm{dB}\\left({V_{pp}^2}\\right)+4\\approx\\mathrm{dB}\\left({V^2}\\right)+10\\approx\\mathrm{dB}\\left({V_{rms}^2}\\right)+13<\/pre><\/div>\n\n\n\n
This happens a lot during calibration. An oscilloscope needs a 500Mhz signal at \"600mV_{pp}\" to test if the front-end rolls off too early (i.e. have a lower bandwidth than advertised), yet my $12k RF signal generator (20Ghz sweeper) only does dBm, and in coarse increments of 0.1dBm.<\/p>\n\n\n\n