# An FSK and OOK Compatible RF Demodulator for Wake Up Receivers

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## Abstract

**:**

## 1. Introduction

## 2. Principle of Frequency and Amplitude Demodulation with an LC Oscillator

#### 2.1. Non-Coherent Demodulation of a Frequency Modulated Signal

_{1}and f

_{2}as illustrated in Figure 2.

_{1}or f

_{2}, and extract the amplitude of the signal by envelope detection. The data are then constructively generated by comparison of V

_{amp2}(t) and V

_{amp1}(t) signals. The frequency deviation, which is the shift between the two discrete frequencies f

_{1}and f

_{2}, is usually in the range of few tens to few hundreds of kHz. As a consequence, the implementation of the circuits which perform the frequency selection is difficult, expensive and sensitive to process variations in the RF domain. For this reason, the FSK demodulation by frequency discrimination is not exploited in WSN applications.

_{0}, and the two frequencies f

_{1}and f

_{2}. f

_{1}and f

_{2}are located in the roll-off response of the band-pass block which yields a different attenuation for each frequency. Hence, the frequency shift of the incoming FSK signal, S

_{1}, is transformed into amplitude variations in S

_{2}. The data are extracted from S

_{2}with an envelope detector. This signal processing of the FSK signal is illustrated in Figure 5. Since the proposed principle of demodulation is no longer based on frequency discrimination but frequency to amplitude conversion, the constrain on the filter selectivity is relaxed in comparison with the demodulator of Figure 3. One condition to perform the FM to AM transformation is to keep the frequency f

_{0}, in Figure 4, different to the center frequency of the frequency to amplitude conversion block.

#### 2.2. AM-to-FM Conversion and AM-AM Transfer with an LC Oscillator

_{0}, the ideal inverting amplifier, in the feedback path, ensures a close loop gain of unity and a total phase shift of 2π.

#### 2.2.1. Injection of a FM Signal

_{inj}(Figure 6) are properly chosen, the circuit keeps on oscillating at ω

_{0}and injection pulling occurs. Under this condition, the output voltage contains both the injected signal and the free-running oscillation. To derive the analytic expressions of the output voltage under the injection of a modulated signal, we assume the simplified expression (Equation (1)) for the tank impedance.

_{p}) the tank losses and Q the tank quality factor. For the first case of study, we consider an injected FM signal I

_{FM}Equation (2):

_{c}and ω

_{m}are respectively the carrier frequency and modulating frequency, β is the modulation index. The instantaneous phase and pulsation are derived as it follows:

_{out}:

_{c}instead of ω

_{0}because the injection locking occurs. Under this condition, the output voltage (V

_{out}) and the injected current (I

_{Inj}) must bear a phase difference φ

_{out}and satisfy the conditions of Equation (10):

_{out}Equation (12a) in Equation (12b) the oscillator locking range can be derived according [6,9], it is reported in Equation (13).

_{out}Equation (12a) is not modulated by the instantaneous frequency of the injected FM signal. As a consequence, the FM-to-AM conversion does not occur, and the demodulation of an FM signal is not possible.

#### 2.2.2. Injection of an AM Signal

_{c}and ω

_{m}are respectively the carrier frequency and modulating frequency, α is the modulation index.

_{out}is derived under pulling condition in Equation (15) and locking injection in Equation (16). A maximum amplitude is obviously achieved when the oscillator is locked.

_{1}in Figure 4, into an AM output signal S

_{2}. The data are transferred in the envelope of S

_{2}, and extracted by an envelope detector. In locked mode, the frequency to amplitude conversion does not occur, the demodulation of an FM signal is not possible in such a mode. In the case of an AM injected signal S

_{1}, it is transferred to S

_{2}with a maximum amplitude in locked mode, the data are then demodulated by envelope detection.

## 3. Implementation of a MOOD Demodulator

#### 3.1. Low Power LC Oscillator

_{tank}and C

_{tank}, sets the free running oscillation of the oscillator, which is fine tuned by C

_{var}. The cross-coupled pair (M

_{2a}, M

_{2b}) compensates for the loss of the tank and sustains the oscillation. The transistors M

_{2i}are sized to operate in moderate inversion region to achieve a best trade-off between performances and current consumption according [12]. The transistor M

_{1}steers the tail current and injects the external signal RF

_{in}applied to its gate. The inductors L

_{g}and L

_{s}perform the 50 Ω input matching. A micrograph of the oscillator, implemented for a stand-alone characterization, is presented in Figure 8c.

**Figure 8.**Schematic of an LC cross-coupled oscillator with RF injection (

**a**); device size (

**b**); micrograph of the oscillator (

**c**).

**Figure 9.**Oscillator Tuning Range versus V

_{tune}(

**a**); Phase Noise at 1MHz versus bias current (

**b**) Oscillator performances at VDD = 0.5 V; & I

_{bias}= 248 μA (

**c**).

_{in}(Figure 8a). The output power of the oscillator, P

_{out}, is represented in Figure 10a as a function of Δf, which is the deviation between the frequency of the CW signal and the free running frequency of the oscillator. For large frequency deviations, the output spectrum follows the free running response as it operates in pulled mode. Figure 10b represents the maximum FM to AL conversion gain (CG

_{FM-AM}) of the oscillator in pulled mode. The figures, extracted from Figure 10a, are valid for a frequency shift of the FM signal equals to half of the corresponding frequency deviation Δf. CG

_{FM-AM}strongly depends on the quality factor of the resonator, and it dramatically decreases when Δf exceeds 50 MHz. Within a frequency range of 2 MHz centered to the free running frequency, the oscillator is locked. The minimum power required to lock the oscillator is measured, and represented in Figure 10b for different Δf. We can note the smaller the frequency deviation, the lower is the power required to lock the oscillator. At a Δf = 20 MHz, a minimum power of −15 dBm is needed to lock the oscillator, for larger frequency deviations the locking power linearly increases with Δf with a slope of 0.25 dB/MHz. This analysis figures out that the sensitivity of a MOOD demodulator operating in locking mode is improved when the free running frequency of the oscillator is tuned to the carrier frequency of the incoming AM signal.

**Figure 10.**P

_{out}in dBm versus Δf = |f

_{LO}− f

_{RFin}| with P

_{RFin}= −31 dBm & f

_{LO}= 2.48 GHz (

**a**); FM to AM Conversion Gain (

**b**); P

_{RFin}to lock the oscillator versus Δf = |f

_{LO}− f

_{RFin}| (

**c**).

#### 3.2. Envelope Detector Design

_{1}is biased in weak inversion, as the drain current of a MOS transistor is an exponential function of gate-source voltage in this region. M

_{2}acts as a simple current source to bias M

_{1}with a constant current. A large capacitor C

_{f}is connected to node V

_{out}. The bandwidth at the output is derived in Equation (17). It is set by the pole f

_{p,det}formed by C

_{f}, and the output impedance of the detector which is approximately (1/g

_{m1}) neglecting the body effect:

_{p,det}is adjusted to twice the maximum data rate of the demodulated signal.

**Figure 11.**Differential ED implemented in the MOOD demodulator (

**a**); single ED implemented as a standalone circuit for characterization (

**b**); micrograph of the single ended ED in 65 nm CMOS (

**c**).

_{in}in Figure 11b. Since the output bandwidth is much smaller than the input signal frequency, the full signal appears across the gate-source terminal V

_{GS}of M

_{1}. M

_{1}, biased in WI region, generates an output current that is an exponential function of the input voltage. To further investigate the circuit of Figure 11b, an equivalent model is proposed in Figure 12. The exponential function, expanded with Taylor series and dropping terms above the second order, acts as a squaring function. It actually transforms the AC amplitude of V

_{in}into a DC current i

_{0}. The fundamental frequency, along with higher order harmonics, of V

_{in}will be filtered out by C

_{f}. Although higher order terms will also generate DC components, these contributions are small compared to the squaring term. The output impedance R

_{o}is simply 1/g

_{m1}.

_{1}operating in weak inversion is modeled as [14]:

_{0}is a constant depending on process and device size, V

_{th}is the threshold voltage, V

_{t}is the thermal voltage (kT/q), and n is the subthreshold slope factor. Expanding Equation (18) in Taylor series and focusing on the second order term, the DC component i

_{0}of I

_{D}is expressed in Equation (19):

_{in}, the expression of a sine wave (V

_{s}sin(ω

_{s}t)) with g

_{m}= I

_{D}/nV

_{t}, the DC component i

_{0}, Figure 17, becomes:

_{p,det}, and the output voltage of the detector V

_{out}is expressed as Equation (21):

_{det}, is finally the ratio of the output DC voltage V

_{out}to the peak AC amplitude V

_{s}of V

_{in}:

_{s}. This analysis holds for small input signals where the response is dominated by the second order term and higher order effects are not significant. The measured conversion gain, GC

_{det}, is illustrated in Figure 13b. If the amplitude of the input signal is kept below 200 mV, GC

_{det}is close to 0dB and the expression (Equation (22)) gives a good approximation of it. If the amplitude is larger than 400 mV the conversion gain rolls off, and the small signal analysis is no longer correct. To preserve the dynamic of demodulated data, the amplitude of the AM signal at the input of envelope detector would not exceed 500 mV.

**Figure 13.**AC gain (

**a**); AC to DC conversion gain CG

_{det}versus the input amplitude V

_{s}(

**b**) of the envelope detector.

## 4. Characterization of MOOD Demodulator

#### 4.1. Demodulation of Amplitude and Frequency Modulated Signals

_{m}and the carrier power level P

_{carrier}are respectively fixed to 200 kHz and −12 dBm. The free running frequency, f

_{OL}, is set to 2.48 GHz. The measured peak-to-peak amplitude of the output voltage (V

^{PP}) at base band is reported in Figure 15a, for an amplitude modulated (AM) input signal, in Figure 15b, for a frequency modulated (FM) input signal.

**Figure 15.**Peak-to-peak output voltage V

^{PP}versus carrier frequency for modulation depth (m in %) with an AM input signal (

**a**); an FM input signal (

**b**).

^{PP}increases with the modulation depth for the two types of modulation. In the case of an AM signal, Figure 15a, the AM to AM conversion (V

^{PP}) smoothly increases as the carrier frequency gets closer to the free running frequency f

_{OL}. When the oscillator is locked, dashed box in Figure 15a, the AM to AM transfer is maximum, the best efficiency yields at m = 100% with a V

^{PP}of 350 mV, which corresponds to a voltage gain of 6 dB. In the case of an FM input signal, Figure 15b, the frequency shift is converted into amplitude variation, we observe the amplitude of the output voltage V

^{PP}decreases as the carrier frequency gets closer to the free running frequency f

_{OL}. When the oscillator is locked, dash box in Figure 15b, the frequency to amplitude conversion does not occur and V

^{PP}is zero, the FM signal is not demodulated.

_{m}is illustrated in Figure 16. The carrier frequency (f

_{carrier}) and power (P

_{carrier}) are fixed, the output amplitude V

^{PP}is measured for different f

_{m}. For the AM test, the oscillator is locked to achieve a maximum AM-to-AM transfer. According to Figure 16a, V

^{PP}is maximum if the f

_{m}frequency is kept below 300 kHz. Above this frequency the demodulated signal is attenuated by the bandwidth of envelope detector. For the FM test, Figure 16b, the oscillator is operated in pulled mode, and the sensitivity is maximum for a f

_{m}of 380 kHz.

**Figure 16.**Peak-to-peak output voltage V

^{PP}versus the modulating frequency f

_{m}with an AM input signal (

**a**); an FM input signal (

**b**).

#### 4.2. FSK and OOK Demodulation

_{b}) and carrier power (P

_{carrier}) are respectively fixed to 20 kbps and −18 dBm, only the carrier frequency f

_{RF}changes. The amplitude of the demodulated data is larger in locked mode 8 mV, Figure 17a, compared to pulled mode 5 mV, Figure 17b. In Figure 17c the oscillator is locked, but the data rate is increased to 500 kbps. The wave form of the demodulated data is distorted by the cutoff frequency of the envelope detector. The bandwidth of the ED limits the maximum data rate in this case.

**Figure 17.**Demodulated data versus original data in locked mode at a data rate of 20 kbps (

**a**); in pulled mode at a data rate of 20 kbps (

**b**); in locked mode at a data rate of 500 kbps (

**c**).

**Figure 18.**Demodulated data versus original data in locked mode (

**a**); in pulled mode at a data rate of 100 kbps and frequency shift Δf = 100 kHz (

**b**); in pulled mode at a data rate of 100 kbps and frequency shift Δf = 1 MHz (

**c**).

_{out}) reaches 12 dB. This sensitivity can be significantly improved with the introduction of a Low Noise Amplifier before the MOOD circuit. The demodulators presented in [15,16], Table 1, do not use any active RF function, which drastically reduces the power consumption to respectively 0.1 μW and 10 μW. To our knowledge, the demodulator presented in [15] exhibits the lowest power consumption reported in the literature. The introduction of a low noise amplification stage before the envelope detector, significantly improves the sensitivity as demonstrated in [4]. It also costs an extra power consumption of 40 μW. The receivers reported in [4,15,16] are based on envelope detectors, which limit the compatibility to OOK modulated signals. The reference [17] proposes a WuRx dedicated to the demodulation of FSK. It features a digitally controlled oscillator coupled with an envelope detector. The power consumption is 45 μW, which is large with respect to the operating frequency 80 MHz, and compared to OOK solutions. The demodulation of an FSK signal requires RF functions that burden the power budget of the receiver.

**Table 1.**Modulated oscillator for envelope detection (MOOD) performances and comparison with the state of the art.

This Work | [15] | [4] | [16] | [17] | ||
---|---|---|---|---|---|---|

Process | 130 nm | 130 nm | 90 nm | 180 nm | 180 nm | |

Frequency | 2.4 GHz | 915 MHz | 2 GHz | 2.4 GHz | 80 MHz | |

Power Consumption | 120 μW | 0.1 μW | 52 μW | 10 μW | 45 μW | |

VDD | 0.6 V | 1.2 V | 0.5 V | 0.5 V | 0.7 V | |

Modulation | OOK | FSK | OOK | OOK | OOK | FSK |

Data rate | 150 kbps | 300 kbps | 100 kbps | 100 kbps | 100 kbps | 300 kbps |

Sensitivity | −36 dBm | −27 dBm | −41 dBm | −72 dBm | −65 dBm | −62 dBm |

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Taris, T.; Kraimia, H.; Belot, D.; Deval, Y.
An FSK and OOK Compatible RF Demodulator for Wake Up Receivers. *J. Low Power Electron. Appl.* **2015**, *5*, 274-290.
https://doi.org/10.3390/jlpea5040274

**AMA Style**

Taris T, Kraimia H, Belot D, Deval Y.
An FSK and OOK Compatible RF Demodulator for Wake Up Receivers. *Journal of Low Power Electronics and Applications*. 2015; 5(4):274-290.
https://doi.org/10.3390/jlpea5040274

**Chicago/Turabian Style**

Taris, Thierry, Hassène Kraimia, Didier Belot, and Yann Deval.
2015. "An FSK and OOK Compatible RF Demodulator for Wake Up Receivers" *Journal of Low Power Electronics and Applications* 5, no. 4: 274-290.
https://doi.org/10.3390/jlpea5040274