## 4 Space-Qualified RF Generator Techniques
### SSB Mixing  
Another more unconventional technique is the use of the Single Side Band (SSB) approach. This mixing principle is a proven technique [39; 40; 41] and can also be used in the frame of space applications [42]. In this approach, a reference oscillator signal \(f_{c}\) is used, shifted by \(90^{\circ}\) and applied to two separate mixing devices (Figure 9). The incoming signal [\(V_{IN}cos(2\pi f_{IN}t)\)], in which V\({}_{\rm IN}\) represents the amplitude of the input voltage and \(f_{IN}\) the frequency of the input signal, is also shifted by \(90^{\circ}\) and applied to  
Figure 8: DDS RF generator harmonics and spur levels for different frequencies. Figure 9: SSB principle. the two mixing devices. Both outputs (\(s_{1}\) and \(s_{2}\)) are summed, which creates the requested RF output signal \(s_{OUT}\). The signal in the upper chain can be written as  
\[s_{1}=V_{IN}\cdot V_{C}\cdot cos(2\pi f_{IN}t)\cdot\cos(2\pi f_{C}t) \tag{7}\]  
in which \(V_{C}\) is the amplitude of the oscillator signal and \(f_{C}\) the frequency of the oscillator. For the lower chain, the following signal is formed:  
\[s_{2}=V_{IN}\cdot V_{C}\cdot sin(2\pi f_{IN}t)\cdot sin(2\pi f_{C}t) \tag{8}\]  
Rewriting these formulas generates  
\[s_{1}=\frac{V_{IN}\cdot V_{C}}{2}\cdot\left\{\cos[2\pi(f_{C}+f_{IN})t]+\cos[2 \pi(f_{C}-f_{IN})t]\right\} \tag{9}\]  
\[s_{2}=\frac{V_{IN}\cdot V_{C}}{2}\cdot\left\{\cos[2\pi(f_{C}-f_{IN})t]-\cos[2 \pi(f_{C}+f_{IN})t]\right\} \tag{10}\]  
Adding up or subtracting both signals generates the \(RF\) output signal \(s_{OUT}\):  
\[s_{OUT}=V_{IN}\cdot V_{C}\cdot cos[2\pi(f_{C}-f_{IN})t], \tag{11}\]  
or  
\[s_{OUT}=V_{IN}\cdot V_{C}\cdot cos[2\pi(f_{C}+f_{IN})t] \tag{12}\]  
Equation (9) is known as the Lower Side Band (LSB) signal, and Equation (10) as the Upper Side Band (USB) signal. Hence, the output frequency can be generated from \(f_{C}-f_{IN}\) (for the LSB setting) up to \(f_{C}+f_{IN}\) (for USB setting). Based on this technique, a bread frequency range can be covered. An example of a space implementable SSB design for the VIS range is shown in Figure 10. The \(f_{IN}\) signal can be generated using a DDS inside an FPGA. This approach is explained in paragraph B. The selected space-qualified FPGA can be an RTAX, which runs at a frequency of 127 MHz. Hence, an output signal can be generated after the DAC of 50 MHz, taking the theorem of Nyquist into account [31; 32]. The reference oscillator runs at a higher frequency compared to the RTAX-DAC combination. For each optical wavelength domain (VIS, NIR, and UV), a dedicated reference oscillator and RTAX-DAC combination is needed. E.g., for the VIS range (Figure 7), the RTAX-DAC runs at 30 MHz with a reference oscillator at 90 MHz. Hence, a frequency  
Figure 10: SSB setup for the VIS range. range generated at the output falls between 60 MHz (=90 MHz \(-\) 30 MHz, applying the LSB setting) and 120 MHz (=90 MHz + 30 MHz, applying the USB setting). The different building blocks in Figure 10 are all available as space-qualified components. A clear disadvantage of this approach is the amount of building blocks. Hence, the used mass, volume, and PCB area are rather high. In total, the power consumption is around 2.2 W for the FPGA and DACs, while, due to the high amount of passive building blocks, the attenuation is around 15 dB [42]. The generated output frequency at 90.001 MHz using a 90 MHz reference oscillator and a 1 kHz DDS signal in the USB setting shows many different harmonics and spurs (Figure 11). The suppression of these signals is at barely \(-\)30 dB. The output power level of the RF signal is rather low (around \(-\)15 dBm). This requires an additional RF amplifier block at the output of the RF generator in order to fulfill the \(>\)0 dBm requirement. This will again consume the PCB area, mass, volume, and power. The frequency resolution depends on the resolution of the DDS inside the FPGA. Due to the small steps achievable in a DDS setup (see paragraph 4.2), the frequency resolution can be met easily.