**4. System noise floor and conclusion**

To evaluate the noise floor, we designed the platform when the test signal and reference signal were distributed in phase from a single signal generator. The signal generator at 10MHz and the beat-frequency value of 100Hz were set. For this example obtained the Allan deviation (square root of the Allan variance (DAVID A, HOWE)) of ( ) 4.69 14 V *y* W*E* at

$$\tau = 1 \text{ second} \text{ and } \sigma\_y(\tau) = 1.27E-15 \text{ at } \tau = 1000 \text{ second.}$$

The measurement ability could be optimized further by improving the performance of OG. Because the reference of the system is drove by the output of OG.

Since the digital correlation techniques can smooth the effects of random disturbance of the MBFG, it can achieve higher measurement accuracy than other methods even if on the same MBFG.

128 Applications of Digital Signal Processing

2 2

) )

*ij ij*

2 2 1

*B B*

*B B*

*ij ij*

<sup>1</sup> <sup>2</sup> 2 1 cos ( ) ( ) cos( )

' ) )

*N NN*

*N NN*

2 2 1

*<sup>g</sup>* represent standard deviation of Gaussian random variable, Signal Noise Ratio

, and here the V is the amplitude of input signal, let amplitude resolution of a-bit

1 12 2 cos ( ) ( ) 4 12 *e ij*

*<sup>e</sup>* is the standard deviation of measurement initial phase difference. The standard

deviation of digital correlation algorithms depends on the sampling frequency N, SNR and amplitude resolution 'a', as understood from formula (3.26). Here the noise of amplitude resolution can be ignored if the 'a' is sufficiently bigger than 16-bit and the SNR is smaller than 100 dB. The measurement accuracy for this method is mostly related to SNR of signal. This method has been tested that has the strong anti-disturbance

To evaluate the noise floor, we designed the platform when the test signal and reference signal were distributed in phase from a single signal generator. The signal generator at 10MHz and the beat-frequency value of 100Hz were set. For this example obtained the Allan deviation (square root of the Allan variance (DAVID A, HOWE)) of ( ) 4.69 14

second.

The measurement ability could be optimized further by improving the performance of OG.

Since the digital correlation techniques can smooth the effects of random disturbance of the MBFG, it can achieve higher measurement accuracy than other methods even if on the same

 *E* at 1000 W

Because the reference of the system is drove by the output of OG.

2 2

*N N*

0

 

¦

*B*

(3.25)

2 1 *<sup>a</sup> V* ' ( Ken

V *y* W *E* at

*B*

*N*

*m N*

*m*

0

2 2

' ) (3.26)

2

*V N SN* ¦

1 2 2 0

1 1 cos ( ) ( cos( ) )

¦

*g*

V

*g*

*g*

digitize and quantization step be ' , here variable 'a' can be 8~24. We have <sup>2</sup>

Mochizuki, 2007). Applying this equation to formula (3.25) term by term, we obtain

2

V

1 1( cos ( ) cos( ) )

*N ij ij m*

*N*

) )

1

*N*

*m*

*N*

Where <sup>2</sup> V

*<sup>V</sup> SN* V

Where

capability.

W

MBFG.

V

2 2 *g* 0

¦

4

4

2

4 12

*ij*

*ij*

' )

<sup>1</sup> <sup>2</sup> 2 1 cos ( ) ( ) 4 12 1 2 2 cos ( ) ( ) 4 12

' d )

V

2

2

V

**4. System noise floor and conclusion** 

 1 second and ( ) 1.27 15 V *y* W

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Additional, the design of calibration channel that is proposed to remove the systematic error is useful to acquire better performance for current application. A comprehensive set of noise floor tests under all conditions has not been carried out with the current system.

The system hardware consists only of MBFG, DAQ and PC. Compared with the conventional systems using counter and beat-frequency device, the system can be miniaturized and moved conveniently. As expected, system noise floor is good enough for current test requirement. The system will take measurement of wide range frequency into account in the future. Intuitive operator interface and command remotely will be design in following work.
