To obtain the Power Spectral Density (PSD) from a dB value measured by a spectral analyzer, you need to know the reference power level or reference impedance of the instrument used to make the measurement. The PSD is defined as the power per unit frequency, typically expressed in units of dBm/Hz or dBV/Hz.
Here's the general process to convert a dB value to PSD:
Determine the reference power level or reference impedance of the spectral analyzer. This information is typically provided in the instrument's specifications or user manual. For example, it could be stated as "Reference level: 0 dBm" or "Reference impedance: 50 ohms."
Convert the dB value measured by the spectral analyzer to a linear scale. To do this, you need to use the reference level or reference impedance. The formula to convert dB to a linear scale is: Linear Value = Reference Value * 10^(dB Value/10)
For example, if the reference level is 0 dBm and you have a measurement of -40 dBm, the linear value would be: Linear Value = 1 mW * 10^(-40 dBm/10) = 0.0001 mW = 0.1 µW
Once you have the linear value, you can convert it to the PSD by dividing it by the bandwidth over which the measurement was made. The bandwidth is typically given in Hz. The formula to calculate PSD is: PSD = Linear Value / Bandwidth
For example, if the measurement was made over a bandwidth of 1 kHz (1000 Hz), the PSD would be: PSD = 0.1 µW / 1000 Hz = 0.1 nW/Hz
If desired, you can convert the PSD value to dBm/Hz or dBV/Hz by taking the logarithm of the PSD value: PSD (dBm/Hz) = 10 * log10(PSD in Watts/Hz) + 30 (for dBm) or PSD (dBV/Hz) = 10 * log10(PSD in Volts^2/Hz) + 20 (for dBV)
Note: The +30 or +20 terms are added to convert the values from Watts/Hz or Volts^2/Hz to dBm/Hz or dBV/Hz, respectively.
Please ensure that you have the appropriate units and references for your specific spectral analyzer and measurement setup. Refer to the instrument's documentation for detailed instructions or consult with the manufacturer's support if you need further assistance.