NAPiCOS enables to measure micro weight molecule using mass loading effect of quartz crystal sensor. Quartz crystal sensor has a feature that it oscillates resonance frequencies stably with thickness shear vibration. When a substance put on the electrode and adsorbed on the electrode plate of the crystal sensor, the frequency of the vibration is decreased corresponding to the weight. This is known as mass loading effect.

Sauerbrey equation is relational one between mass and frequency.

1．Sauerbrey equation

Sauerbrey equation is often used as relational one between mass and frequency for uniform and solid items like thin membrane .,A calculation for mass and thickness of the thin membrane at vacuum evaporation is one of the examples. According to Sauerbrey equation, 1Hz frequency shift amount is equivalent for approximately 1ng/cm2, at usage of NDK's 9MHz crystal sensor.

2．Kanazawa-Gordon equation

In the case of mass loading effect of chemical reaction in liquid phase, Kanazawa-Gordon equation is generally used. In liquid with too much viscosity, resonance series resistance of crystal is big due to the viscosity. The viscosity is considered in Kanazawa-Godon equation.

Reference：K.Keiji Kanazawa and JOSEPH G.GORDON Ⅱ －Analytica Chmica Acta(1985)99-105

3．Positioning of equation from perspective of quartz crystal engineering

Quartz crystal sensor has more factors beside the above mentioned ones, and so is much influenced with measurement method and environment etc. Relational equation between rigorous mass and frequency of immune reaction in liquid is still unclear. So, combination of Sauerbrey equation and Kanazawa-Gordon one should be recommended.

NAPiCOS measurement is advanced one of conventional QCM method and captures resonance frequency as micro mass change according to frequency shift obtained from oscillation and other measurement circuit.

First of all, frequency, as one of NAPiCOS's features, was defined as frequency stability by the declaration of IRE (Currently IEEE F.C.S.) special team, and shall comply with IEEE Standard 1139-1999. The standard includes short term stability (1 second or less) and long term stability (1 second or more). This is widely known as general intelligence to "Institute of Electrical Engineers of Japan (IEE)" and related sections of frequencies in "The Institute of Electronics, Information and Communication Engineers (IEICE)."

Moreover, NAPiCOS is technically electrical measurement equipment. Accuracy of frequency measurement is defined by JIS C 1002 and JIS C 1005 based on IEC standard. In the case of deviance from the standard, consideration for absolute value of mass would be difficult. For example, the frequency counter displays 1Hz /sec. When measurement is made with frequency counter at 9,000,000Hz and 1sec.gate, 9,000,000Hz is not guaranteed due to an error of 9,000,000Hz ±1Hz. From the point of guarantee of frequency absolute value, 9,000,000Hz is not guaranteed with the oscillator on which short term stability down to 0.1Hz digit is not guaranteed, in spite of frequency measurement down to 0.1Hz digit. Generally,1Hz frequency shift at 9,000,000Hz is equivalent for a new ngs of mass shift. This is based on that accuracy 9,000,000Hz ±0.1Hz is guaranteed. So, frequency measurement accuracy is very much important.

Due to a stress-sensitivity principle of crystal blank, micro amount of frequency shift like 0.1Hz may easily occurs, when rolling capability of solution, vortex of solution ,or gas or air stream exist at side of crystal chip with protein formation.

Crystal unit is main part of sensor, and a quality grade of the crystal blank should be strictly selected. The electrode material is strictly selected too so that it may fit to the crystal blank. The crystal blank.Is asymmetry one..So, designs for axis direction, outward form, dimensions electrode thickness, cutting angle etc. should be made to conform to the protein to be measured. If this is not followed. some problems may come up such as unstable frequency as measurement value, sudden frequency shift , no repeatability etc..

Relative equation between frequency shift amount and reaction amount is based on Sauerbrey one. Solution viscosity etc. is not considered in Sauerbrey equation .This means that Sauerbrey equation is not well considered one from the point of crystal unit design. Moreover, application of energy confinement effect is not well considered .So, value result obtained should be carefully checked.

Moreover, measurement method for frequency and resonance resistance via using network analyzer and impedance analyzer has been suggested by other party. In the case of measurement with the method, inaccurate values may be obtained such as impedance matching specifically shown in high frequency measurement and increased shift velocity between frequency and phase originated from decreased Q conducted by viscous material formation on the crystal unit surface etc..

NAPiCOS, suggested by NDK, newly researched and developed measurement system from the poit of frequency absolute values, frequency measurement, crystal blank design and crystal unit design, for which frequency rigor , definition of frequency measurement are strictly applied.