# 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 Highly Linear Harmonic Receiver  
The first problem in creating a highly linear harmonic receiver is that the measurement hardware is itself nonlinear. The RF front end of a spectrum analyzer consists of nonlinear devices such as amplifiers and mixers. For the results presented in this paper, a National Instruments (NI) (Austin, TX, USA) PXIe-5668R spectrum analyzer is used. The 5668R is specified to generate a second harmonic >69 dBc down from the fundamental, between 700 to 1000 MHz with 0-dBm input power [45]. Although the data sheet specifies >69 dBc, the measured self-generated second harmonic is 80 dBc. This 80 dBc of dynamic range is sufficient to make harmonic measurements of strongly nonlinear devices, such as amplifiers, mixers, and diodes, but is inadequate to make measurements of weakly nonlinear elements. The first example of this shown in Figure 3, which depicts an ideal probe signal entering an amplifier. In Figure 3, \"DUT\" stands for \"device under test\", \"HPF\" stands for \"high-pass filter\", and \"LPF\" stands for \"low-pass filter\". The DUT is a Mini-Circuits amplifier ZX60-3018G-S+. The fundamental and harmonic responses are made on the PXIe-5668R spectrum analyzer. The choice of filters is very important in architecting a reliable harmonic measurements system [46]. Figure 2: Illustration of the relationship between OIP\({}_{2}\) and \(D_{2}\). Three different low-pass filter options are tested using the setup in Figure 3. These include: (1) no filter; (2) a Mini-Circuits reflective filter VLF-1200; and (3) a Mini-Circuits diplexer RPB-272. When no filter is used, the dynamic range of the test setup is set by the spectrum analyzer, namely 80 dBc. The dynamic range of test setup is increased by filtering out the fundamental frequency before it enters the spectrum analyzer. For every 1-dB attenuation of the fundamental, the self-generated second harmonic of the spectrum analyzer decreases 2 dB. This follows from the relationship in Equation (3). A commercial off-the-shelf (COTS) Mini-Circuits high-pass filter VHF-1200 would be a natural choice, but most COTS filters attenuate the stop band frequencies by creating an impedance mismatch. The result of the mismatch is that the undesired frequencies are reflected and not passed through the filter. The impact of this is examined later. To attenuate the fundamental frequency and to reduce the reflection back into the DUT, a diplexer is used. The low frequency port is terminated in 50 \(\Omega\). For this setup, the probe signal is set to 800 MHz and the probe signal power is calibrated to be \(-\)20 dBm at the input to the amplifier. The resolution bandwidth (RBW) on the spectrum analyzer was set to 800 Hz and the internal attenuator was set to 30 dB. The results in Table 1 illustrate the following two concepts: (1) the spectrum analyzer has the dynamic range to measure the second harmonic response from the Mini-Circuits amplifiers; and (2) the reflective filter alters the test setup and yields false results. If the input power to the spectrum analyzer is 0 dBm, the spectrum analyzer will generate a second harmonic on the order of \(-\)90 dBm. Therefore, the reading of \(-\)36.3 dBm is well above the self-generation level of the setup and it is a valid reading. To measure lower level harmonics, the dynamic range of the system needs to be increased. This can be done by using a filter. When a reflective filter is used, the undesired probe signal is reflected causing a reverse traveling wave that enters the output port of the DUT. Once the probe signal enters the output port of the DUT, the probe signal generates additional nonlinearities. The results in Table 1 show more than a 7-dB increase in the measured second harmonic when the reflective filter is used. Figure 4 illustrates this reflection and additional generation of the second harmonic when a reflective filter is used.