*3.2. Proposed CR-ILFD*

Figure 6 shows a schematic of the proposed CR-ILFD, consisting of a fourth-order resonator (*L*1, *C*1, *L*2, *C*2), distributed inductor (*L*3), injection switch (M3), CR core (M1, M4), center-tap generator (M2, M5), and output buffer. *Vinj,DC* and *Vinj,*<sup>2</sup>*w* are the input signals, whereas *Vout,w* is the output signal. The center-tap generator biases the node of the primary coil, *L*1 to *VCT*. If the gm matching of PMOS and NMOS is well adjusted, mathematically, *VCT* would be *VDD*/2. The DC value of the injection switch can be biased to *VCT* without additional supply, but it was not connected for measurement. The distributed inductor is employed to extend the locking range of the ILFD. The distributed inductor is also referred to as the inductor distributed technique [28,29]. The magnitude of the load impedance can be increased by distributing the primary inductor into two series inductors.

**Figure 6.** Schematic of the proposed CR-ILFD.

Figure 7a shows the simulated magnitude plot and phase plot of the fourth-order resonator-based ILFD and the proposed CR-ILFD with the fourth-order resonator with a distributed inductor. The start-up condition in Figure 7a is determined by the "Barkhausen formula" in (12). In the case of the fourth-order resonator-based ILFD, an unlocking part may occur because of the minimum value that is less than the start-up condition. However, the magnitude of the load impedance is sufficiently increased by using the inductor distributed technique. Figure 7b shows the slightly increased phase. This is not a critical amount of change because the phase ripple still exists between the ±*φ*max. The simulated locking range of the proposed ILFD is from 21.6 to 37.4 GHz, which is limited by the ±*φ*max in (11).

**Figure 7.** (**a**) Simulated magnitude plot and (**b**) phase plot of the fourth-order resonator-based ILFD and proposed CR-ILFD.

Figure 8 shows an equivalent model of the fourth-order resonator using a transformer with the distributed inductor. Figure 8a shows a model including the parasitic capacitors and resistors of the passive components. Zin is the input impedance and "*k*" is the coupling factor between *L*1 and *L*2. *Cp*1, *Rp*1, *Cp*2, and *Rp*2 represent the parasitic components. In the mm-Wave band, the analog circuits are affected more by electromagnetism. Therefore, the modeling of the resonator must be considered at the initial design stage. Because analyzing every parasitic component is difficult, modeling should be simplified by approximation as shown in Figure 8b. *CT*1 is the sum of *Cp*1 and *C*1. Similarly, *CT*2 is the sum of *Cp*2 and *C*2. Additionally, the Q factor of the inductor includes the parasitic resistances. *Vt* and It are the test voltage and test current, respectively. *Vt*/*It* is equal to *Zin* in the simplified model. The value of *Zin* is calculated as follows.

$$Z\_{in}(\mathbf{s}) = \frac{(1 - k^2)L\_1 L\_2 \mathbb{C}\_{T2} \mathbf{s}^3 + L\_1 \mathbf{s}}{(1 - k^2)L\_1 L\_2 \mathbb{C}\_{T1} \mathbb{C}\_{T2} \mathbf{s}^4 + (L\_1 \mathbb{C}\_{T1} + L\_2 \mathbb{C}\_{T2}) \mathbf{s}^2 + 1} \times (1 + 2L\_3 \mathbb{C}\_{T1} \mathbf{s}^2). \tag{19}$$

**Figure 8.** (**a**) Modeling of the fourth-order resonator using a transformer with distributed inductor. (**a**) Modeling of including the parasitic capacitors and resistors. (**b**) Approximate modeling applied to simplify calculations.

If the distributed inductor (*L*3) is zero, then (19) is equal to (15). That is, the distributed inductor does not directly affect the pole value in (17), and if the distributed inductor value is increased, the magnitude of *Zin* can be increased.

The design parameters are listed in Table 1. Because the center-tap generator should not limit the core operation, the width of the center-tap generator should be significantly larger than that of the CR core. The parasitic capacitor of the center-tap generator is separated from the resonator and does not affect the operating frequency. The sizes of the CR core and injection switch are not only determined by (11) and (12), but also by the influence of the parasitic capacitors.

**Table 1.** Design parameters of the proposed CR-ILFD.


Figure 9 shows a flowchart of the design approach for the proposed CR-ILFD. First, the equivalent circuit model must be implemented in the simulator. Second, the values of the design parameters should be determined. In the proposed CR-ILFD, the center frequency is set to receive an injection signal of 28 GHz. Because the distributed inductor does not directly affect the pole value, the values of *L*1, *C*1, *L*2, *C*2 and k are first determined. Subsequently, *L*1 is divided into two series inductors, *L*1 and *L*3. In this design, *L*1, *L*2, and *L*3 are 230, 265, and 433 pH, respectively. *C*1 and *C*2 are 144 and 240 fF, respectively. The value of k is 0.51. When *k* < 0.5, which represents a weak coupling, the distance between

the poles increases, and a wide magnitude plot of the load impedance can be obtained. However, a coupling that is too weak can cause an unlocking part in which the ILFD does not work. Considering the locking range and unlocking part, the proposed CR-ILFD is designed with a coupling factor of 0.51. Finally, the layout and locking simulation are repeated in the order shown in the flowchart. Electromagnetic simulation is essential in the mm-Wave band. Therefore, it should be ensured that the difference between the equivalent modeling and implementation in the simulation of this circuit is reasonable.

**Figure 9.** Flowchart of the design approach for the proposed CR-ILFD.

## **4. Measurement Results**

Figure 10 shows the die photograph of the proposed CR-ILFD, which was fabricated in a 65 nm CMOS technology. The die size including the entire pad is 0.75 mm × 0.45 mm and the chip size including the core and output buffer is 0.49 mm × 0.3 mm. The measurement setup for the proposed CR-ILFD is shown in Figure 11. The measurements were obtained using a probe station. The DC voltage was biased from the power supply. The CR core of the proposed CR-ILFD consumes 2.26 mW from a 1 V supply voltage, when no signal is applied to the injection switch. As *Vinj,DC* increases, the power consumption increases. When *Vinj,DC* is 0.7 V, the power consumption of the core increases by approximately 0.5 mW. The power consumption of the output buffer is approximately 3 mW. The injection signal was generated by Anritsu MG3694, which can generate frequencies up to 40 GHz. The output signal of the proposed CR-ILFD is analyzed by KEYSIGHT N9030B, which can analyze frequencies up to 50 GHz. When conducting measurements using mm-Wave signals, several losses occur around the device under test (DUT). Therefore, the calibration tests must be carried out carefully. In this measurement, the ground–signal–ground (GSG) probe tip has a loss of approximately 2.5 dB and that of the radio frequency (RF) cable has

approximately 3 dB. Approximately a 1 dB loss occurs even when the signal generator output is 10 dBm. The loss of the signal generator was analyzed by connecting the signal analyzer and RF cable. All losses described above are based on the 28 GHz signal. Generally, the loss increases as the frequency increases, and decreases as the frequency decreases.

**Figure 10.** Die photograph of the proposed CR-ILFD.

**Figure 11.** Measurement setup for the proposed CR-ILFD.

Figure 12a shows the measured locking range of the proposed CR-ILFD with different *Vinj,DC* values. The maximum locking range is from 18.8 to 33.8 GHz (57%) at *Vinj,DC* of 0.7 V. When the *Vinj,DC* is biased to 0.6 V, the locking range is from 19.2 to 34.4 GHz (56.7%), and when the *Vinj,DC* is biased to 0.5 V, the locking range is reduced from 22.7 to 34.6 GHz (41.5%). The above ranges were obtained from 0 dBm input power and 1 V supply voltage. As the *Vinj,DC* decreases, the locking range also tends to decrease. Figure 12b shows a comparison of the measured and simulated locking range results of the proposed CR-ILFD. The measured locking range is 57%, and simulated locking range is from 21.6 to 37.4 GHz (53.6%). When 0 dBm input power is injected to the CR-ILFD, the measured locking range is typically changed to a lower frequency band than the simulated locking range. The operating frequency band was lowered by approximately 3 GHz. This is because of various electromagnetic components, such as RF pads, printed circuit board (PCB), and metal lines that were not considered in the simulations. The measured maximum operation frequency is higher when the input power is −3 dBm compared to when the input power is 0 dBm. This is because of the saturation of the input signal level.

**Figure 12.** (**a**) Measured locking range results of the proposed CR-ILFD with different Vinj,DC; (**b**) measured and simulated locking range results of the proposed CR-ILFD.

Figure 13a shows the measured maximum and minimum operation frequencies of the proposed CR-ILFD with different *Vinj,DC* values. This measurement was carried out with 0 dBm input power and 1 V supply voltage. *Vinj,DC* is swept from 0.4 to 1.2 V, and the widest locking range is obtained at the *Vinj,DC* of 0.7 V. When *Vinj,DC* increases from 0.7 V, the maximum and minimum operation frequencies decrease, and the locking range also decreases.

**Figure 13.** (**a**) Measured maximum and minimum operation frequency of the proposed CR-ILFD with different *Vinj,DC*; (**b**) Measured phase noise of input and output signal.

The measured phase noise of the input and output signal is shown in Figure 13b. The 28 GHz input signal is generated by Anritsu MG3694, which is applied to the proposed CR-ILFD and the output signal is 14 GHz. The phase noise of the output signal is −109.57 and −129.81 dBc/Hz at 100 kHz and 1 MHz offset frequency, respectively. The phase noise of the output signal should be measured at 6 dBc/Hz lower than that of the input signal because the input signal frequency is twice that of the output signal. Figures 14 and 15 show the results of several spectrums of the CR-ILFD's output signal measured using the KEYSIGHT N9030B. The spectrum of the output signal when the proposed CR-ILFD self-oscillates is shown in Figure 14a. The output frequency is 14.08 GHz, and output

power is −10.45 dBm. If the loss of the RF cable and GSG probe tip is calibrated, the output power will be approximately −5 dBm. The spectrum of the output signal when the 28 GHz input signal is injected to the proposed CR-ILFD is shown in Figure 14b. The frequency of the output signal is 14 GHz, which is exactly half the frequency of the input signal. The output power is approximately −8 dBm with loss calibration. Figure 15a shows the full span spectrum when the minimum input frequency, 18.8 GHz, is injected. Three tones are visible in the spectrum: the output signal (f0), input signal (2f0), and harmonic signal (3f0). As shown in Figure 3, several harmonic components are amplified at output when the minimum input frequency is injected to the CR-ILFD. Locking is possible even if a lower input frequency is injected. However, the input signal is amplified such that the power difference from the output signal is less than 10 dB. When 18.8 GHz is injected, the power difference between the desired output signal and the harmonic signal is approximately 10 dB. Figure 15b shows the full span spectrum when the maximum frequency input signal of 33.8 GHz is injected. The power difference between the output and input signals is more about 20 dB. It can be observed that the amplified input signal is smaller when the maximum input frequency is injected than when the minimum input frequency is injected. As a result, harmonic rejection ratio of the input signal over the entire locking range is more than 10 dBc.

**Figure 14.** Spectrums of the output signal (**a**) when the proposed CR-ILFD self-oscillates; (**b**) when the proposed CR-ILFD is locked with a 28 GHz injection signal.

**Figure 15.** Full span spectrums (**a**) when the minimum input frequency is injected (18.8 GHz); (**b**) when the maximum input frequency is injected (33.8 GHz). The power difference between the output and input signals is approximately 10 dB or more.

> Table 2 summarizes the performance comparison of different core ILFDs. These include challenging and typical ILFD cores such as Darlington [30], Armstrong [31], Collpits [32], and cross-coupled pair [33–35]. This work has the highest figure of merit (FOM) compared to other ILFDs presented in Table 2.



*Sensors* **2021**, *21*, 2551

high band).

Table 3 summarizes the performance comparison of the mm-Wave ILFDs [36–41]. ILFDs with division ratio greater than two are also included such as four [37,38] and six [41], but still have the highest FOM1 values.


**Table 3.** Performance comparison of mm-Wave ILFDs.

\*: Total locking range (low band + high band), \*\*: Only core size.
