The sensitive technique, adopted in the photo-multiplication measurement, requires a reference signal at a fixed frequency. This is used in the lock-in amplifier to generate a reference signal at the same frequency. The diagram illustrating the signals in a phase sensitive detection is shown in . and are the phases of the measured signal and the θsig θref lock-in amplifier reference signal. The measured signal and lock-in amplifier reference signal have the expression as follows. (3.4) (3.5) and are the amplitudes of the measured signal and reference signals. The output of Asig Aref this sensitive detection is the product of the two sine waves, given by (3.6) When the output passed through a low pass filter, the AC component in equation 3.6 with Vo the frequency at will be filtered out, leaving the low frequency component with + ωsig ωref frequency at When = the output would be a DC signal - Asig Aref ωsig ωref. ωsig ωref, Therefore, the measured signal with same frequency component to the cos(θsig - θref). reference signal will be isolated with output amplitude proportional to the measured signal amplitude. Figure 3.4 Diagram of phase sensitive technique When the measured signal is a square wave with amplitude of at frequency it can be Ap f, considered to be sum of many harmonic sinusoid at multiples off as (3.7) The first sinusoid wave component will be measured and displayed in its RMS value of 2Ap/π × /2 = This technique could avoid any low frequency noise from high leakage or Ap/π. tunnelling current. The avalanche gain, dependent on voltage can be derived by
The sensitive technique, adopted in the photo-multiplication measurement, requires a reference signal at a fixed frequency. This is used in the lock-in amplifier to generate a reference signal at the same frequency. The diagram illustrating the signals in a phase sensitive detection is shown in . θsig and θref are the phases of the measured signal and the lock-in amplifier reference signal. The measured signal and lock-in amplifier reference signal have the expression as follows. (3.4) (3.5) Asig and Aref are the amplitudes of the measured signal and reference signals. The output of this sensitive detection is the product of the two sine waves, given by (3.6) When the output Vo passed through a low pass filter, the AC component in equation 3.6 with the frequency at ωsig + ωref will be filtered out, leaving the low frequency component with frequency at ωsig - ωref. When ωsig = ωref, the output would be a DC signal Asig Aref cos(θsig - θref). Therefore, the measured signal with same frequency component to the reference signal will be isolated with output amplitude proportional to the measured signal amplitude. Figure 3.4 Diagram of phase sensitive technique When the measured signal is a square wave with amplitude of Ap at frequency f, it can be considered to be sum of many harmonic sinusoid at multiples off as (3.7) The first sinusoid wave component will be measured and displayed in its RMS value of 2Ap/π × /2 = Ap/π. This technique could avoid any low frequency noise from high leakage or tunnelling current. The avalanche gain, dependent on voltage can be derived by
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