Neper

The neper \(\textrm{(Np)}\) is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals.

Like the decibel, the neper is a unit in a logarithmic scale. While the bel uses the decadic (base-10) logarithm to compute ratios, the neper uses the natural logarithm.

The level \(L\) of a ratio of two signal amplitudes or root-power quantities, with the unit neper \(\textrm{(Np)}\).

\(\boxed{L = \ln\left(\frac{a}{b}\right)}\quad\textrm{Np}\)

where \(a\) and \(b\) are the signal amplitudes.

The level \(L\) of a ratio of two power quantities, with the unit neper \(\textrm{(Np)}\).

\(\boxed{L = \frac{1}{2}\ln\left(\frac{p_1}{p_2}\right)}\quad\textrm{Np}\)

where \(p_1\) and \(p_2\) are the signal powers.

The decibel \(\textrm{(dB)}\) and the neper \(\textrm{(Np)}\) have a fixed ratio to each other.

\(\boxed{1\:\textrm{Np} = 20\log_{10}(e)\:\textrm{dB}}\)

\(\boxed{1\:\textrm{dB} = \frac{1}{20}\ln(10)\:\textrm{Np}}\)

Like the decibel, the neper is a dimensionless unit.

Links to this page
  • Step Response of a Series RLC Circuit

    where roots \(s_1\) and \(s_2\) are called natural frequencies, measured in nepers per second \((\textrm{Np}/\textrm{s})\); \(\omega_0\) is known as the resonant frequency or strictly as the undamped natural frequency, expressed in radians per second \((\textrm{rad}/\textrm{s})\); \(\alpha\) is the neper frequency or the damping factor, expressed in nepers per second \((\textrm{Np}/\textrm{s})\); \(R\) is the equivalent resistance; \(L\) is the equivalent inductance; and \(C\) is the equivalent capacitance.

    where \(\omega_0\) is the undamped natural frequency and \(\alpha\) is the neper frequency.

  • Step Response of a Parallel RLC Circuit

    where roots \(s_1\) and \(s_2\) are called natural frequencies, measured in nepers per second \((\textrm{Np}/\textrm{s})\); \(\omega_0\) is known as the resonant frequency or strictly as the undamped natural frequency, expressed in radians per second \((\textrm{rad}/\textrm{s})\); \(\alpha\) is the neper frequency or the damping factor, expressed in nepers per second \((\textrm{Np}/\textrm{s})\); \(R\) is the equivalent resistance; \(L\) is the equivalent inductance; and \(C\) is the equivalent capacitance.

    where \(\omega_0\) is the undamped natural frequency and \(\alpha\) is the neper frequency.

  • Source-Free Series RLC Circuit

    where roots \(s_1\) and \(s_2\) are called natural frequencies, measured in nepers per second \((\textrm{Np}/\textrm{s})\); \(\omega_0\) is known as the resonant frequency or strictly as the undamped natural frequency, expressed in radians per second \((\textrm{rad}/\textrm{s})\); \(\alpha\) is the neper frequency or the damping factor, expressed in nepers per second \((\textrm{Np}/\textrm{s})\); \(R\) is the equivalent resistance; \(L\) is the equivalent inductance; and \(C\) is the equivalent capacitance.

    where \(\omega_0\) is the undamped natural frequency and \(\alpha\) is the neper frequency.

  • Source-Free Parallel RLC Circuit

    where roots \(s_1\) and \(s_2\) are called natural frequencies, measured in nepers per second \((\textrm{Np}/\textrm{s})\); \(\omega_0\) is known as the resonant frequency or strictly as the undamped natural frequency, expressed in radians per second \((\textrm{rad}/\textrm{s})\); \(\alpha\) is the neper frequency or the damping factor, expressed in nepers per second \((\textrm{Np}/\textrm{s})\); \(R\) is the equivalent resistance; \(L\) is the equivalent inductance; and \(C\) is the equivalent capacitance.

    where \(\omega_0\) is the undamped natural frequency and \(\alpha\) is the neper frequency.

  • Damping

    where \(\omega_0\) is known as the resonant frequency or strictly as the undamped natural frequency, expressed in radians per second \((\textrm{rad}/\textrm{s})\); and \(\alpha\) is the neper frequency or the damping factor or the damping attenuation, expressed in nepers per second \((\textrm{Np}/\textrm{s})\).

#power #unit