A Sub-GHz Multi-ISM-Band ZigBee Receiver Using Function-Reuse and Gain-Boosted N-Path Techniques for IoT Applications

Abstract

Internet of Things (IoT) represents a competitive and large market for short-range ultra-low-power (ULP) wireless connectivity [1, 2]. According to [3], by 2020 the IoT market will be close to hundreds of billion dollars (annually ~16 billions). To bring down the hardware cost of such massive inter-connections, sub-GHz ULP wireless products compliant with the existing wireless standard such as the IEEE 802.15.4c/d (ZigBee ) will be of great demand, especially for those that can cover all regional ISM bands [e.g., China (433 MHz), Europe (860 MHz), North America (915 MHz) and Japan (960 MHz)]. Together with the obvious goals of small chip area, minimum external components and ultra-low-voltage (ULV) supply (for possible energy harvesting), the design of such a receiver poses significant challenges.

Appendices

Appendix A: Output-Noise PSD at BB for the N-Path Tunable Receiver

The derivation of the output-noise PSD at BB due to R_S, 4G_m, R_sw and R_F1 is presented here. The model used to obtain the NTFs is shown in Fig. 5.17. For all output-noise PSDs, there are two parts: one is the direct transfer from input RF to BB, while another is from harmonics folding noise. For the latter, increasing the path number N can reduce such contribution. The differential output-noise PSD for R_s, 4G_m, R_sw and R_F1 with $\overline{{ {\text{V}}_{{{\text{n}},{\text{R}}_{\text{S}} }}^{2} }} = 4{\text{KTR}}_{\text{s}}$, $\overline{{{\text{V}}_{{{\text{n}},4{\text{Gm}}}}^{2} }} = {\raise0.7ex\hbox{${4{\text{KT}}}$} \!\mathord{\left/ {\vphantom {{4{\text{KT}}} {{\text{g}}_{{{\text{m}}1}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${{\text{g}}_{{{\text{m}}1}} }$}}$, $\overline{{{\text{V}}_{{{\text{n}},{\text{Rsw}}}}^{2} }} = 4{\text{KTR}}_{\text{sw}}$ and $\overline{{{\text{V}}_{{{\text{n}},{\text{R}}_{{{\text{F}}1}} }}^{2} }} = 4{\text{KTR}}_{{{\text{F}}1}}$ are given as (A.1)–(A.4),

Fig. 5.17

Equivalent noise model of the N-path tunable receiver (Fig. 5.3d) for BB output-noise PSD calculation and simulation. N = 4 is used. The noise sources g_m1 and R_F1 from the 4G_m are explicitly shown

$$ \overline{{{\text{V}}_{{{\text{n}},{\text{out}},{\text{R}}_{\text{S}} }}^{2} }} = \left\{ {\underbrace {{\left| {{\text{H}}_{{ - 1,{\text{R}}_{\text{S}} }} \left( {{\text{j}}\omega } \right){\text{V}}_{{{\text{n}},{\text{R}}_{\text{S}} }} \left( {{\text{j}}\omega + \omega_{\text{s}} } \right)} \right|^{2} }}_{{{\text{Part}}\,{\text{A}}}} + \underbrace {{\sum\limits_{{{\text{n}} = - \infty ,{\text{n}} \ne - 1}}^{\infty } {\left| {{\text{H}}_{{{\text{n}},{\text{R}}_{\text{S}} }} \left( {{\text{j}}\omega } \right){\text{V}}_{{{\text{n}},{\text{R}}_{\text{S}} }} \left( {{\text{j}}\left( {\omega - {\text{n}}\omega_{\text{s}} } \right)} \right)} \right|^{2} } }}_{{{\text{Part}}\,{\text{B}}}}} \right\} \times 4 $$

(A.1)

$$ \overline{{{\text{V}}_{{{\text{n}},{\text{out}},4{\text{Gm}}}}^{2} }} = \left\{ {\underbrace {{\left| {{\text{H}}_{{ - 1,4{\text{Gm}}}} \left( {{\text{j}}\omega } \right){\text{V}}_{{{\text{n}},4{\text{Gm}}}} \left( {{\text{j}}\omega + \omega_{\text{s}} } \right)} \right|^{2} }}_{{{\text{Part}}\,{\text{A}}}} + \underbrace {{\mathop \sum \limits_{{{\text{n}} = - \infty ,{\text{n}} \ne - 1}}^{\infty } \left| {{\text{H}}_{{{\text{n}},4{\text{Gm}}}} \left( {{\text{j}}\omega } \right){\text{V}}_{{{\text{n}},4{\text{Gm}}}} \left( {{\text{j}}\left( {\omega - {\text{n}}\omega_{\text{s}} } \right)} \right)} \right|^{2} }}_{{{\text{Part}}\,{\text{B}}}}} \right\} \times 4 $$

(A.2)

$$ \overline{{{\text{V}}_{{{\text{n}},{\text{out}},{\text{R}}_{\text{sw}} }}^{2} }} = \left\{ {\underbrace {{\left| {{\text{H}}_{{ - 1,{\text{R}}_{\text{sw}} }} \left( {{\text{j}}\omega } \right){\text{V}}_{{{\text{n}},{\text{R}}_{\text{sw}} }} \left( {{\text{j}}\omega + \omega_{\text{s}} } \right)} \right|^{2} }}_{{{\text{Part}}\,{\text{A}}}} + \underbrace {{\mathop \sum \limits_{{{\text{n}} = - \infty ,{\text{n}} \ne - 1}}^{\infty } \left| {{\text{H}}_{{{\text{n}},{\text{R}}_{\text{sw}} }} \left( {{\text{j}}\omega } \right){\text{V}}_{{{\text{n}},{\text{R}}_{\text{sw}} }} \left( {{\text{j}}\left( {\omega - {\text{n}}\omega_{\text{s}} } \right)} \right)} \right|^{2} }}_{{{\text{Part}}\,{\text{B}}}}} \right\} \times 4 $$

(A.3)

$$ \overline{{{\text{V}}_{{{\text{n}},{\text{out}},{\text{R}}_{{{\text{F}}1}} }}^{2} }} = \left\{ {\underbrace {{\left| {{\text{H}}_{{ - 1,{\text{R}}_{{{\text{F}}1}} }} \left( {{\text{j}}\omega } \right){\text{V}}_{{{\text{n}},{\text{R}}_{{{\text{F}}1}} }} \left( {{\text{j}}\omega + \omega_{\text{s}} } \right)} \right|^{2} }}_{{{\text{Part}}\,{\text{A}}}} + \underbrace {{\mathop \sum \limits_{{{\text{n}} = - \infty ,{\text{n}} \ne - 1}}^{\infty } \left| {{\text{H}}_{{{\text{n}},{\text{R}}_{{{\text{F}}1}} }} \left( {{\text{j}}\omega } \right){\text{V}}_{{{\text{n}},{\text{R}}_{{{\text{F}}1}} }} \left( {{\text{j}}\left( {\omega - {\text{n}}\omega_{\text{s}} } \right)} \right)} \right|^{2} }}_{{{\text{Part}}\,{\text{B}}}}} \right\} \times 4 $$

(A.4)

For the above NTFs, the even order terms (including zero) of n are excluded. The single-ended HTFs for R_S, 4G_m, R_sw and R_F1 are ${\text{H}}_{{{\text{n}},{\text{R}}_{\text{S}} }} \left( {{\text{j}}\omega } \right), {\text{H}}_{{{\text{n}},4{\text{Gm}}}} \left( {{\text{j}}\omega } \right),\,{\text{H}}_{{{\text{n}},{\text{R}}_{\text{sw}} }} \left( {{\text{j}}\omega } \right)\,{\text{and}}\,{\text{H}}_{{{\text{n}},{\text{R}}_{{{\text{F}}1}} }} \left( {{\text{j}}\omega } \right)$, respectively. Further details were covered in [11].

Appendix B: Derivation and Modeling of BB Gain and Output Noise for the Function-Reuse Receiver

When considering the memory effect of the capacitor C_i and C_o with R_F3 sufficiently large, the voltages (i.e., the circuit states) at C_i are independent [19]. In the steady-state, around the clock frequency, the voltages sampling at C_i are υ_Ci(t), jυ_Ci(t), –υ_Ci(t), –jυ_Ci(t), while the voltage sampling at C_o is υ_CO(t), jυ_CO(t), –υ_CO(t), –jυ_CO(t), for LO_1–4, respectively. When LO₁ is high (K = 1), linear analysis shows the following state-space description for capacitor C_i,

$$ \left\{ \begin{aligned} & \left\{ {\begin{array}{*{20}c} {\frac{{{\text{C}}_{\text{i}} {\text{d}}\upupsilon_{\text{Ci}} \left( {\text{t}} \right)}}{\text{dt}} = \left( {\upsilon_{{{\text{B}}1,{\text{I + }}}} \left( {\text{t}} \right) +\upupsilon_{{{\text{B}}1,{\text{I - }}}} \left( {\text{t}} \right) +\upupsilon_{{{\text{B}}1,{\text{Q + }}}} \left( {\text{t}} \right) +\upupsilon_{{{\text{B}}1,{\text{Q}} - }} \left( {\text{t}} \right)} \right)g_{\text{m3}} } \\ { +\upupsilon_{{{\text{B}}1,{\text{Q - }}}} \left. {\left( {\text{t}} \right)} \right){\text{g}}_{{{\text{m}}3}} } \\ { + \left( {\upupsilon_{{{\text{B2}},{\text{I + }}}} \left( {\text{t}} \right) +\upupsilon_{{{\text{B2}},{\text{I}} - }} \left( {\text{t}} \right) +\upupsilon_{{{\text{B2}},{\text{Q + }}}} \left( {\text{t}} \right)} \right)} \\ { + \left. {\upupsilon_{{{\text{B2}},{\text{Q}} - }} \left( {\text{t}} \right)} \right)\frac{1}{{4{\text{R}}_{\text{L}} }}} \\ \end{array} } \right. \\ & \frac{{\upupsilon_{\text{RF}} \left( {\text{t}} \right) -\upupsilon_{\text{Ci}} \left( {\text{t}} \right)}}{{{\text{R}}_{\text{s}} }} = \frac{{{\text{C}}_{\text{i}} {\text{d}}\upupsilon\left( {\text{t}} \right)}}{\text{dt}} \\ & \quad \quad\upupsilon_{\text{i}} \left( {\text{t}} \right) =\upupsilon_{\text{Ci}} \left( {\text{t}} \right) +\upupsilon_{\text{o}} \left( {\text{t}} \right) + {\text{R}}_{\text{sw}} \frac{{{\text{C}}_{\text{i}} {\text{d}}\upupsilon\left( {\text{t}} \right)}}{\text{dt}} \\ & \quad \quad\upupsilon_{\text{i}} \left( {\text{t}} \right) -\upupsilon_{{{\text{B}}1,{\text{I + }}}} \left( {\text{t}} \right) =\upupsilon_{\text{Ci}} \left( {\text{t}} \right) \\ & \quad \quad\upupsilon_{\text{i}} \left( {\text{t}} \right) -\upupsilon_{{{\text{B}}1,{\text{I - }}}} \left( {\text{t}} \right) = -\upupsilon_{\text{Ci}} \left( {\text{t}} \right) \\ & \quad \quad\upupsilon_{\text{i}} \left( {\text{t}} \right) -\upupsilon_{{{\text{B}}1,{\text{Q + }}}} \left( {\text{t}} \right) = {\text{j}}\upupsilon_{\text{Ci}} \left( {\text{t}} \right) \\ & \quad \quad\upupsilon_{\text{i}} \left( {\text{t}} \right) -\upupsilon_{{{\text{B}}1,{\text{Q}} - }} \left( {\text{t}} \right) = - {\text{j}}\upupsilon_{\text{Ci}} \left( {\text{t}} \right) \\ & \quad \quad\upupsilon_{\text{o}} \left( {\text{t}} \right) +\upupsilon_{\text{co}} \left( {\text{t}} \right) =\upupsilon_{{{\text{B}}2,{\text{I}} + }} \left( {\text{t}} \right) \\ & \quad \quad\upupsilon_{\text{o}} \left( {\text{t}} \right) -\upupsilon_{\text{co}} \left( {\text{t}} \right) =\upupsilon_{{{\text{B}}2,{\text{I}} - }} \left( {\text{t}} \right) \\ & \quad \quad\upupsilon_{\text{o}} \left( {\text{t}} \right) + {\text{j}}\upupsilon_{\text{co}} \left( {\text{t}} \right) =\upupsilon_{{{\text{B}}2,{\text{Q}} + }} \left( {\text{t}} \right) \\ & \quad \quad\upupsilon_{\text{o}} \left( {\text{t}} \right) - {\text{j}}\upupsilon_{\text{co}} \left( {\text{t}} \right) =\upupsilon_{{{\text{B}}2,{\text{Q}} - }} \left( {\text{t}} \right) \\ \\ \end{aligned} \right. $$

(B.1)

Equation (B.1) can be simplified similar to (5.1). Likewise, when LO₁ is low, it can be described by (5.4). Thus, it has the same BB HTFs as in gain-boosted N-path SC network [shown also in (5.8)].

The BB NF at V_B2,I± (V_B2,Q±) is approximately modeled in Fig. 5.18. The BB output noise at V_B1,I± (V_B1,Q±) are further amplified by two separate BB amplifiers, while in the function-reuse receiver they are amplified by the same BB amplifiers. From simulations, with a large R_F3, the model has a good accuracy, while for a small R_F3, the error increases for the low-frequency part. This is because the BB gain at V_B1,I± (V_B1,Q±) gets smaller under a small R_F3, and the independent noise sources from the model’s G_m contribute additional noise (Fig. 5.19a, b). The function-reuse receiver has a smaller NF and requires lower power than the separated G_m situation. For the BB gain, this model has a high accuracy (not shown).

Fig. 5.18

Schematic to model the BB NF of the functional-reuse receiver at V_B2,I±

Fig. 5.19

Simulated BB NF from the model and functional-reuse receiver with a a small R_F3 and b a larger R_F3