2 January 2010 0 Comments

Radio Frequency Specifications: Dynamic Range & Bandwidth

Dynamic Range

The radar receiver must be capable of handling large signals from surface reflections and short-range targets and also detect small signals near the noise floor. The ratio of the largest receivable signal to the minimal detectable signal is called the dynamic range and is defined as follows:

\textrm{Dynamic Range}=20\,\log\left(\frac{V_{\max}}{V_{\min}}\right)

It is usually expressed in decibels (dB) for a specified bandwidth in hertz. The largest receivable signal, V_{\max} (in V), must not overload the radar front end and, assuming some gain has been applied to the received signal, is the maximum sample voltage of the ADC. Additionally, for a CW GPR, the largest signal is defined by the 1-dB compression point of the receive mixer where the gain deviates from linearity. This assumes no saturation after the mixer.

The minimal detectable signal, V_{\min} (in V), must be above the receiver noise level and have a minimum signal-to-noise ratio (SNR) to be detected. In most radar detection applications, an SNR of 8 dB is required (Erst, 1985). In most GPR applications, V_{\min} must also have a minimum signal-to-clutter ratio (SCR) in order to be detected and identified in a GPR profile.

The dynamic range of the system will affect the maximum range at which a target can be detected. Typically, radars will have a greater system dynamic range than sampling dynamic range. The dynamic range in decibels of an ADC is equal to 20\,\log\left(2^{N}\right), where N is the number of bits, or approximately N times 6 dB. Thus, a 16-bit ADC will have 96 dB of theoretical dynamic range, but other factors influence the actual realizable dynamic range.

Bandwidth

The system bandwidth, $$B$$, is defined as the inverse of the pulse width, $$\tau_{p}$$, for impulse GPR. The bandwidth is generally centered about and for practical reasons is approximately equal to the impulse GPR center frequency, $$f_{c}$$. The center frequency is a very common GPR parameter and is the answer to the universal question: “what frequency did you use?”

In a CW GPR, the bandwidth is the difference from the start frequency, $$f_{\min}$$, to the stop frequency, $$f_{\max}$$, and can also be calculated by multiplying the number of steps by the output frequency step size in a stepped frequency GPR. The bandwidth ultimately determines the range resolution
B=\frac{1}{\tau_{p}}\qquad\textrm{for impulse}
or
B=\left(f_{\max}-f_{\min}\right)\qquad\textrm{for CW}

Reference

Jol, H. M. Ground penetrating radar : theory and applications Elsevier Science, 2009,

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