# Hardware Design of a High Dynamic Range Radio Frequency (RF) Harmonic Measurement System
## 3 Issues in Creating a High Dynamic Range Harmonic Measurement System
### Creating a Harmonic Free Probe Signal
#### 3.2.1 Filter Considerations  
The amount of second harmonic present in probe signal can never reach zero, or \(-\infty\) dB. Therefore, it can only be attenuated to the noise floor of the measurement setup. As in Section 3.1, the linearity of the measurement system can be increased by filtering. The NI PXI-5651 signal generator used is specified to produce less than 25 dBc of second harmonic when the output power is 0 dBm [47]. We assumed this value does not change too much when the output power is increased to +10 dBm. With +10 dBm of output power, the 5651 signal generator will produce less than \(-15\) dBm of second harmonic, thereby providing 25 dBc of dynamic range. Thus, if this generator is used without any filtering, accurate second harmonic measurements are made to \(-5\) dBm, including the 10-dB safety factor for signal-to-interference ratio, which is not very useful when trying to make sensitive harmonic measurements. To increase the dynamic range of the receiver, a low-pass filter is used. For the probe signal, the improvement in dynamic range is a 1:1 ratio. So, if the signal generator provides a 25-dBc dynamic range and 160 dBc is desired, the attenuation required for the low pass filter is 145 dB. The general expression for the attenuation needed by the low pass filter is:  
\[A_{L}=\text{DR}_{d}-\text{DR}_{g}+10 \tag{6}\]  
where \(A_{L}\) is the attenuation required of the low-pass filter at the second harmonic and \(\text{DR}_{g}\) is the dynamic range of the signal generator. Again, a 10-dB safety factor is built in to ensure 10 dB of signal-to-interference ratio.  
Most COTS filters do not provide greater than 100 dB of attenuation required to linearize the probe signal. Therefore, multiple filters need to be cascaded to achieve the large attenuation required. As stated in Section 3.1, most COTS filters are reflective, and attenuation is achieved in the stop band by an impedance mismatch causing the stop band frequencies to reflect backwards and not pass through it. This reflective nature of filters causes problems.  
The Mini-Circuits low-pass filter, Model # VLF-1200, has a cut off frequency of 1 GHz. However, the stop band of this filter does not meet the >100-dB attenuation requirement. Therefore, multiple filters need to be cascaded to increase the stop band attenuation. Figure 6 shows the measured and theoretical \(|S_{21}|\) response when two VLF-1200 filters are cascaded. The theoretical cascaded \(|S_{21}|\) response was computed as a product of the individual \(|S_{21}|\) responses.  
When the two reflective low-pass filters are cascaded, the measured and theoretical responses do not closely match. This point is further investigated in [48], where three reflective low pass filters are cascaded. The measured results when three low-pass filters are cascaded show more discrepancy when compared to the theoretical response.  
Figure 6: Measured and theoretical \(|S_{21}|\) response when two VLF-1200 low-pass filters are cascaded.  
Using a number of cascaded reflective filters causes large variations in the measurement system's dynamic range as a function of frequency. If the measurement system operates at a single frequency, a null in the cascaded frequency response can be used. If measurements are taken over a bandwidth of frequencies, the fluctuations in the frequency response would not permit reliable, repeatable, and accurate measurements.