**3. Designs**

Figure 3 shows the architecture of the MedRadio RF receiver. It is designed in an RF CMOS process. The receiver comprises a low-noise amplifier (LNA), transconductance (Gm) stage, quadrature down-conversion mixer with IM2 calibration, trans-impedance amplifier (TIA) with dc offset calibration (DCOC), three-stage variable gain amplifiers (VGAs), complex bandpass filter (BPF), fractional-N phase-locked loop (PLL) synthesizer, and a divide-by-4 local oscillator (LO) generator.

**Figure 3.** The MedRadio RF receiver architecture.

The receiver takes a low intermediate-frequency (IF) architecture employing a quadrature single down-conversion scheme. The IF frequency is set equal to the channel bandwidth of 300 kHz so that the down-converted IF band resides in 150–450 kHz.

The image band of the desired RF signal is rejected by the complex BPF. As shown in Figure 3, the complex BPF comprises two-stage complex biquads and three-stage VGAs. The detailed block diagram of the single-stage complex biquad is shown in Figure 4a. The unit biquad is based on a modified Tow-Thomas low-pass filter (LPF) structure in which the lossless integrator block (OPA1, C1) is put before the lossy integrator block (OPA2, R3, C3). Since the second-order filtering is given by the unit biquad, the overall two-stage complex BPF presents a fourth-order bandpass filtering characteristics. Figure 4b illustrates how the low-pass characteristics of the unit biquad are translated to the complex bandpass characteristics. The cross-interconnecting resistors Rxa and Rxb that are placed between the I- and Q-path biquads as shown in Figure 4a shift the complex conjugate poles to real poles, resulting in the original low-pass filter response being shifted to the desired complex bandpass filter response, which gives the image rejection capability [25]. For optimal image rejection performance, the center frequency *fo* is equally set to the channel bandwidth. As a result, the image component at the negative frequency band at −*fo* is suppressed with respect to the wanted positive frequency band at <sup>+</sup>*fo*. To cope with process variability and also to support variable channel bandwidth modes, key performance parameters of the complex biquad are tunable by realizing the on-chip resistors and capacitors in a switched value structure. The resulting switched tuning ranges are given by 34–136 kΩ with 2-bit control for R1, 82–103 kΩ with 3-bit control for R3, and 0.6–7.35 pF with 4-bit control for C1 and C3, while R2 and R4 are fixed to 135 kΩ. Then, the overall complex BPF shows a tunable gain of −22–+45 dB, tunable center frequency of 0.25–3 MHz, tunable bandwidth of 0.23–2.7 MHz, and tunable quality factor of 0.9–1.1. In addition, the passband flatness is also tunable by independently controlling the on-chip Rxa and Rxb in the range of 78–106 kΩ so that the band-edge gain difference is adjusted in the range of −1–+1 dB [25].

Figure 4c is the schematic of the operational amplifiers OPA1 and OPA2. It is a fully differential two-stage amplifier with a dc common-mode feedback (CMFB). The first stage is a differential pair having *p*-FET input pair of M1,2 and *n*-FET active load of M3,4, and the second stage is *n*-FET common-source stage of M5,6. Designed parameters of the FET's gate width/length are 200/0.2 μm for M1,2, 80/0.5 μm for M3,4, 64/0.2 μm for M5,6, 192/0.5 μm for M7,8, and 480/0.5 μm for M9. The dc bias currents are 42 μA for M9 and 18 μA for M7,8. The frequency compensating RC and CC are 4 kΩ and 0.9 pF, respectively.

**Figure 4.** Complex biquad. (**a**) Block diagram, (**b**) transfer characteristics, (**c**) operational amplifier schematic.

The LO signal is generated by the fractional-N PLL frequency synthesizer. A 20-bit digital delta-sigma (Δ∑) modulator is employed for the fractional-N frequency generation. Details of this PLL can be found in the author's prior work [26]. The voltage controlled oscillator (VCO) covers 1.4–1.8 GHz, which is 4× higher than the MedRadio RF band of 401–406 MHz. The automatic frequency calibration (AFC) searches for an optimal sub-band out of the 32 sub-bands through 5-bit switched capacitor bank of the VCO. The divide-by-4 LO generator circuit after the VCO buffer generates I/Q LO signals with 25% duty cycle for driving the mixer FETs. The 25% duty-cycle LO signal improves the conversion gain and noise figure performances of the quadrature mixer [17].

Figure 5 shows the detailed circuit schematic of the RF front end. The LNA is based on the single-ended cascode structure with M1,2 (gate width = 128 μm, gate length = 60 nm) and a resistive load RD (408 Ω), dissipating 520 μA. The source degeneration inductor Ls of 9 nH and the additional gate-to-source capacitor Cgsx of 0.74 pF are used for simultaneous noise and power matching. The input impedance matching is achieved only by a single off-chip inductor Lext (132 nH). The Gm stage with M4,5 (gate width = 5.6 μm, gate length = 60 nm) and M6,7 (gate width = 16 μm, gate length = 60 nm) performs a singleto-differential conversion for interfacing between the single-ended LNA and differential mixer. It also prevents a severe degradation of the LNA performance that can be otherwise caused by the low input impedance of the passive mixer. The passive mixer with M11,14 (gate width = 14 μm, gate length = 60 nm) is adopted for the benefits of the low power dissipation and low 1/f noise. The differential I/Q LO signals LOIp,m and LOQp,m are fed to the mixer via ac-coupling capacitors Cb (10 pF).

**Figure 5.** Circuit schematic of the RF front end.

The TIA comprises an operational amplifier A1 and feedback components R1 and C1. The R1 and C1 are designed in a switched value structure for achieving the bandwidth tunability between 3.4 and 9.5 MHz. R1 is switchable among 2, 8, 9, and 10 kΩ, and C1 is switchable between 0 and 3.5 pF with 0.5 step. The A1 is a fully differential two-stage structure with its gain bandwidth product of 21.6 MHz. The total gain of the RF front end is +42.2 dB.

The IM2 calibration at the mixer is designed to minimize the IM2 distortion. It is generally known that the IM2 distortion created by FET non-linearities is manifested by the differential mismatches in FETs, dc bias voltages, passive impedances, and layout routings. Thus, the differential mismatches need be minimized to suppress the IM2 distortion at the receiver output. In this design, as proposed in [27,28], the dc gate bias voltages Vgp and Vgm for the switch FET's M11–14 are controlled by employing a 6-bit R-2R digital-toanalog converter (DAC). The DAC needs to have a fine-tuning resolution for precise IM2 calibration, but a higher number of total bits will make the calibration process slow. Thus, in order to overcome the two conflicting requirements of the fine resolution and lower number of control bits, we set the full scale of the DAC to a significantly reduced value of only 50 mV, while its common-model level is tunable for a wider range between 0.5 and 0.9 V by using another 3-bit DAC. As a result, the gate bias tuning resolution is as fine as 0.78 mV. In this work, the IM2 calibration is done manually by monitoring the IM2 level with respect to the mixer gate bias voltages. In a practical mass-production stage, this IM2 calibration can be done more efficiently by using automatic test equipment (ATE).

IM2 calibration is verified through circuit simulations. Figure 6 shows simulation results. The desired RF input of −30 dBm at 402 MHz is injected, and the OOB twotone blockers of −10 dBm at (420, 421 MHz) in one simulation and (650, 651 MHz) in the other simulation are injected. With the LO frequency set to 404 MHz, the wanted IF signal appears at 2 MHz, while the IM2 distortion appears at 1 MHz. The IM2 distortion power with respect to the wanted tone power is examined with the gate bias voltage Vgp tuned from 0.5 to 1.0 V, while the other gate bias Vgm is fixed at 0.7 V. As can be seen, the IM2 distortion level is drastically reduced when the gate bias voltage Vgp is set to an optimal point, which is 0.65 V for 420/421 MHz blocker and 0.7 V for 650/651 MHz blocker. It clearly implies that any unwanted mismatches that are inevitable during the circuit fabrication processes can be successfully compensated by the proposed IM2 calibration circuit, thus guaranteeing a satisfactory IM2 distortion level in the receiver.

**Figure 6.** Simulation results of the IM2 calibration.

Meanwhile, it is found that the proposed IM2 calibration circuit creates an unwanted dc level change at the mixer output during the IM2 calibration. Since the signals from mixer output to the TIA, the first VGA, and the first biquad are all dc-coupled, the dc level changes at the mixer output will directly lead to a significant dc offset at the first biquad output of the complex BPF. The dc offset must be cancelled out even though the down-converted signal resides in the low-IF band and not in dc. It is because the residual dc offset created by the preceding IM2 calibration will harmfully reduce the dynamic range of the following stages. In the conventional low-IF receiver designs, for example, that reported in [12,29], the signals after the mixer output are ac-coupled. Then, the dc offset can be cancelled out by directly controlling the gate biases of the input FETs of a subsequent stage. However, in this design, that approach cannot be taken because the gate bias tuning will adversely alter the optimum IM2 calibration condition obtained at the previous mixer stage. Thus, in this work, we tune the body bias voltages of the input FETs of A1 to cancel out the dc offset. This approach successfully cancels the dc offset at the biquad output, while avoiding the adverse interaction with the IM2 calibration condition at the mixer.

#### **4. Results and Discussions**

The MedRadio receiver is fabricated in a 65 nm RF CMOS process. A micrograph of the fabricated chip is shown in Figure 7, in which the major building blocks are denotated. Note that the chip includes not only the RF receiver of Figure 3 but also an RF transmitter comprising a divide-by-4 circuit and a class-D power amplifier. However, the design details and measurement results of the RF transmitter are not discussed in this paper because they are out of the scope. Nevertheless, the total die size including the entire receiver and transmitter is 2.46 × 1.26 mm2. The fabricated die is mounted and directly wire-bonded on a printed circuit board for experimental measurements. A single supply voltage of 1 V is used.

**Figure 7.** Chip micrograph.

Figure 8 shows the measured S11 of the receiver. The input impedance bandwidth having S11 < −10 dB is 37.5 MHz between 389.4 and 426.9 MHz. It shows that the single series off-chip inductor Lext shown in Figure 5 is enough to achieve the satisfactory input bandwidth for the MedRadio applications. Note that this external Lext is not changed during the subsequent whole OOB blocker measurements.

**Figure 8.** Measured S11 of the receiver.

The measured gain and noise figure performances of the RF front end are plotted in Figure 9. The measurements were done by probing intermediate test ports at the TIA output. The gain is measured by applying the RF and LO signals by using signal generators and reading the output power level by using a spectrum analyzer (N9030B of Keysight Technologies Inc., Santa Rosa, CA, USA). The measured passband gain of the RF front end is +42.2 dB. As shown earlier in Figure 5, the on-chip feedback components R1 and C1 of the TIA are tunable. By controlling these, the TIA bandwidth is tuned between 3.4 and 9.5 MHz in eight steps. Among them, Figure 9 only displays three selected curves corresponding to the minimum 3.4 MHz, medium 4.9 MHz, and the maximum 9.5 MHz conditions for the TIA bandwidth.

**Figure 9.** Measured gain and noise figure of the RF front end.

For the noise figure measurement, the total output noise power *Pn,out* with the input port terminated by 50 Ω is measured by using the spectrum analyzer. With *Pn,out* and the receiver's power gain GP are known, the receiver noise figure is calculated by (*Pn,out* + 174 dBm/Hz − *GP*). This method is convenient because it does not need a noise source or noise figure meter and also ensures sufficient accuracy because the noise floor level of the spectrum analyzer is more than 30 dB lower than *Pn,out*. The measured noise figure at the low-IF band of 150–450 kHz is given by 3.7–4.5 dB. Assuming that a non-coherent detection for binary frequency shift keying (BFSK) signal is adopted, the minimum required SNR should be 14 dB for achieving a bit error rate (BER) of 10−6. In practice, the minimum BER required by a raw RF radio excluding a digital processor can be as high as ~ 10−<sup>3</sup> [5], and the required SNR for this can be further lower by 3 dB, that is, only 11 dB. However, in order to take various practical errors and margins into account, we decide to use 14 dB for the minimum required SNR in the following discussions. Note that the receiver sensitivity *Psens* is given by

$$P\_{\text{Sens}} = -174(\text{dBm}/\text{FHz}) + NF + 10\log(B) + SNR\_{\text{min}} \tag{9}$$

where *NF* is the receiver noise figure, *B* is the signal bandwidth, *SNRmin* is the minimum required SNR. With *SNRmin* = 14 dB, *B* = 300 kHz, and *NF* = 4.5 dB, the receiver sensitivity *Psens* is calculated to be −100.7 dBm or 2.06 μVrms. This sensitivity performance is comparable to [12,15] and much better than [5,13].

Figure 10 shows the measured frequency responses of the complex BPF. The measured curves exhibit the bandwidth tuning and image rejection performances at a medium gain condition. Although not shown here, the gain is also tunable between −22.5 and +45.4 dB in 24 steps. However, normalized gains are drawn in Figure 10 for the sake of clarity. The bandwidth is tunable between 230 and 2700 kHz in 16 steps by tuning the switched resistor and capacitor components R1, C1, R3, and C3 in Figure 4. Figure 10 only displays the four selected curves out of the total 16 curves. The image rejection ratio can be evaluated by taking the ratio of the two gain values, one at the passband's center-frequency point and the other at its image-frequency point. The resulting image rejection ratio is 26.4–33.3 dB, which is sufficient enough considering that the minimum required SNR is 14 dB.

**Figure 10.** Measured frequency response of the complex BPF.

Figure 11 is the measured phase noise of the PLL synthesizer at the output frequency of 400 MHz. The measured phase noise is −98.7 and −125.3 dBc/Hz at 100 kHz and 1 MHz offsets, respectively. The phase noise performance is comparable to the previously reported similar LC VCOs in [12,17], whereas it is much better than [30] for the same MedRadio applications because of the LC cross-coupled structure rather than the ring oscillator structure.

**Figure 11.** Measured phase noise of the PLL synthesizer.

The IM2 calibration is verified through extensive measurements over more than five samples. All results show reasonably good agreements with acceptable variability. Figure 12a shows the measured spectrum, demonstrating how the IM2 distortion is suppressed by the proposed IM2 calibration. The desired RF single tone of −90 dBm at 403.5 MHz are fed to the receiver together with two-tone blocker of −50 dBm at 433.0 and 433.2 MHz. The receiver is set to a nominal gain condition. Then, the wanted IF and unwanted IM2 tones appear at 300 kHz and 200 kHz, respectively. Before the IM2 calibration, the desired and distortion tones are −47.8 and −48.5 dBm, respectively. After the IM2 calibration is carried out, the desired tone power does not show a noticeable change, whereas the IM2 tone power is significantly reduced from −48.5 dBm to −66.1 dBm. As a result, the signal-to-IM2-distortion ratio is improved from +0.7 dB to +18.3 dB. It implies that before the calibration, the receiver cannot satisfy the 14 dB SNR requirement, but after the calibration, it successfully satisfies the SNR requirement with a sufficient margin of 4.3 dB.

**Figure 12.** IM2 calibration performance measurements. (**a**) Spectrum, (**b**) results over the UHF band.

The IM2 calibration measurements are further carried out over the entire UHF band between 420 MHz and 900 MHz, and the results are plotted in Figure 12b. It is observed that the IM2 distortion is suppressed typically by 15 dB in the range of 8.3–20 dB through the IM2 calibration, while the desired tone remains almost unchanged.

The interference tolerance performances of the receiver against the OOB two-tone blocker are evaluated through the carrier-to-interference ratio (CIR) measurements and plotted in Figure 13. The maximum tolerable CIR is measured as following. First, a −90 dBm desired signal at 403.5 MHz is fed to the receiver, and an OOB two-tone blocker with 200 kHz spacing between 420 and 900 MHz is injected together. Then, the blocker signal power is raised until the output SNR reaches 17 dB. Note that we use a 3 dB higher SNR requirement for this CIR test by considering that any more noise and distortion contributions other than this IM2 distortion can be additionally involved in practice. Then, the ratio of the signal and blocker power at this 17 dB SNR condition is defined as the maximum tolerable CIR. The measured results are plotted in Figure 13. The maximum tolerable CIR indicates the receiver's selectivity performance against the two-tone blocker. As can be seen in Figure 13, the proposed IM2 calibration effectively improves the CIR by 4–11 dB across the UHF band. The CIR after the calibration is −40.2 dBc at 420 MHz, which is very close to the in-band, and gradually improves up to −71.2 dBc as the blocker

frequency moves farther away out of the band. The measured CIR can also be translated to the maximum tolerable two-tone blocker power of −49.8–−18.8 dBm. Then, considering *Poffset* = 6.56 dB as discussed in Section 2, we can conclude that the equivalent OFDM blocker power of −43.2–−12.2 dBm can be tolerated by this RF receiver.

**Figure 13.** Measured maximum tolerable CIR against two-tone blocker.

Another important interference tolerance is against a single tone blocker. The measured results are plotted in Figure 14. The desired signal power is set to −98 dBm at 403.5 MHz, which is 3 dB higher than the sensitivity level. The single-tone blocker signal across the VHF and UHF band is injected together, and its power is raised up to a point such that the output SNR becomes 17 dB in the same reason described earlier. The CIR at a frequency that is only 4 MHz away from the desired tone is found to be −41 dBc, which corresponds to the maximum tolerable single-tone blocker power, is −57 dBm. However, in general, the maximum tolerable CIR shows much better performance as low as −70–−77 dBc for the rest of the band between 50–370 MHz and 430–900 MHz. One exception is observed at a half LO frequency near 200 MHz, where the CIR is observed to be −49 dBc. Although the MedRadio standard [1] does not clearly state this, such a limited set of exceptions would be generally accepted for the overall system operations because it can be avoided through high-level channel classification and a search process as is typically done in the Bluetooth receiver for internet-of-things (IoT) applications [28,29].

**Figure 14.** Measured maximum tolerable CIR against single-tone blocker.

The 1 dB gain desensitization against the single-tone blocker is measured and shown in Figure 15. The worst point appearing at 403.5 MHz corresponds exactly to the inputreferred 1 dB compression power (*IP1dB*) of the receiver, which is −40.8 dBm. As the blocker frequency moves away from the in-band, the 1 dB desensitization power continually grows from −26.7 dBm at 350 MHz to −9 dBm at 100 MHz for the lower band and also from −32.7 dBm at 450 MHz to −16.8 dBm at 900 MHz for the upper band.

**Figure 15.** Measured single-tone 1 dB desensitization.

Key performances of this work are summarized and compared with previous CMOS MedRadio receivers in Table 1. It should be noted that most of the previous works [4,5,12,14–16] did not address the OOB blocker tolerance performances. Only a few works reported selectivity performances. Cho et al. [18] reported an OOB CIR of −30 dBc against the VHF band interference between 30 and 70 MHz, and Ba et al. [12] demonstrated the ACR performance of 15 dB in their MedRadio receiver. Huang et al. [19] reported the CIR of −10 dB in their 915 MHz OOK receiver. Such performances should be compared to the CIR against the single tone blocker of this work. As discussed in Figure 14, this work shows much better performance, which is better than −41 dBc without an exception, or even better than −70 dBc if two exceptions are allowed at the half LO and 4 MHz away in-band frequencies. As can be seen in Table 1, this work is the first reporting the OOB CIR performances against the two-tone and single-tone blockers, which can be translated to the maximum tolerable OOB blocker power levels. Additionally, the maximum tolerable CIR against the two-tone blocker can be translated to the maximum tolerable CIR against the OFDM blocker when the *Poffset* of Equation (8) is taken into account.


**Table 1.** Performance summary and comparison.


**Table1.***Cont.*

1 RF front end gain is +42.2 dB. 2 OOB two-tone blocker frequency at 420–900 MHz. 3 OOB single-tone blocker frequency at 50–370 MHz and 430–900 MHz with two exceptions at the half LO frequency and 4 MHz away in-band frequency. 4 OOB single-tone blocker frequency at30–70MHz.
