# Spintronic RF-Direct on-off Keying Modulation Using a Frequency Division Multiplex
## 3 Design of the Spin Modulator
### Simulation on an OOK Modulation Rate in the STNO
\[d[I_{S}(t)]/dt=(I_{DC}-I_{S}(t)-CI_{S}(t)d[R(t)]/dt)/(CR(t)) \tag{3}\]  
where \(C\) is the capacitance located in parallel with the STNO, and \(R(t)\) is the internal resistance of the STNO. \(I_{S}\) is modulated into the STNO after being delayed by the internal resistance of the STNO and the capacitance, which is a main part of the bias-T circuit, as delineated in Equation (3). In this equation, we defined the internal resistance of the STNO, as expressed in Equation (4). The parallel MR, \(R_{P}\), of the fabricated MTJ pillar is 48 \(\Omega\), and the anti-parallel MR, \(R_{AP}\), is 80 \(\Omega\) according to the magnetization angular momentum of the free layer for MTJ pillar. \[R(t)=(R_{AP}+R_{P})/2-(R_{AP}-R_{P})/2\ cos[\theta(t)] \tag{4}\]  
The transient delay for an STNO oscillation signal obtained from a modulated signal is solved from the LLGS equation, given as Equation (1). \(b_{I}/a_{I}\) is assigned as 0.1 in our simulation. The simulation of Equation (1) is performed by the Runge-Kutta algorithm. The parameters used in our simulation are enumerated as follows: \(\alpha\) = 0.01, \(\gamma\) = 1.85 \(\times\) 10\({}^{11}\) Hz/T [20]. If the RF signal flows through the bias circuit path and the modulating signal output circuit path, the RF signal loss decreases as the capacitor value between the bias circuit and the STNO decreases. Additionally, this capacitor value is related to the setting time of the STNO oscillation signal. In this paper, to reduce RF signal loss while minimizing latency, the capacitor between the bias circuits of STNO is selected as 10 pF. The simulation results for the 10 pF circuit conditions resulted in RF signal loss of \(-\)32 dB and setting time of 16 ns. As RF signal loss is weak, the capacitor value is set to 10 pF based on the setting time. The resulting communication transfer rate was calculated to be constrained to 3.38 Mbps (= 1/296 ns, 16 ns for transmitter, 100 ns + 180 ns = 280 ns for receiver). Figure 8 is the time domain signal transmitted from the transmitter after transmitting OOK signals of the STNO, and signals received from the receiver located at a distance of 10 mm from the transmitter after demodulating the signal. As the third part of equation, the in-plane toque component, in the LLGS equation is affected by the long initial start time, long lag time occurs before generating a spin toque signal. Therefore, we used the measurement AFG3251C for short delayed modulation signal under 1 ns, resulting in the short rising time into 10 ns. Figure 8 displays the measurement results observed from the RF monitor after modulating 1 MHz data together with the simulation results. The experiment results show that a data rate of up to 2 Mbps is obtained at each frequency. This shows that a data rate of up to 4 Mbps is acquired by spintronics RF-direct OOK modulation using an FDM with two STNOs in the array. It should be noted that we proposed a new method, making it possible to easily increase the data rate by actively applying an STNO array structure.