Process Control and Instrumentation
Conversion formula for converting amplitude ratio (AR) into decibels is

Decibel = 20 log10 (AR)
Decibel = 20 loge (AR)0.5
Decibel = 20 log10 (AR)0.5
Decibel = 20 loge (AR)

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Process Control and Instrumentation
Routh test

Criterion is not applicable to systems with polynomial characteristic equation
Can not determine as to how many roots of the characteristics equation have positive real roots
Cannot be used to test the stability of a control system containing transportation lag
Criterion provides information about the actual location of roots

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