# A Low Cost BLE Transceiver with RX Matching Network Reusing PA Load Inductor for WSNs Applications
## 2 Proposed Front-End with RX Matching Network Reusing PA Load Inductor
### PA and PA Matching Network  
In the TX, a switching-type single-ended PA operating in non-linear region is employed for the constant envelope modulation required by BLE, as shown in Figure 2a. The PA is typically powered by a DC-DC convertor with reduced output noise [14; 15] for better PA linearity. This PA composes of three stages of amplification, with two inverters as pre-amplifiers for the gate voltage of NM\({}_{2}\). For the first one, it is placed in proximity to VCO to drive the long signal path between VCO and PA. For the second one, it does not generate a rail-to-rail output signal. The final stage is a cascode-type amplifier, where NM\({}_{2}\) adopts thin gate oxide to obtain input/output isolation. The cascode stage NM\({}_{3}\) increases the output impedance of the PA and employs thick gate oxide to withstand peak drain voltage beyond power supply due to the inductive load [16]. The size of the second inverter, together with NM\({}_{2}\) size and NM\({}_{2}\) gate bias, are carefully chosen to obtain the input signal of NM\({}_{2}\) with appropriate amplitude and operation point, which reduce 2 nd harmonic component while maintain the required output power. Simultaneously, 2 nd harmonic component is further attenuated by 15 dB with the matching network.  
In TX mode, the simplified small signal equivalent circuit diagram of ZTX is shown in Figure 3, and the output impedance can be written as:  
\[Z_{TX}=j\omega L_{1}||R_{D}||R_{I}||\frac{1}{j\omega C_{cr}}||Z_{RX-off}, \tag{2}\]  
\[R_{D}=[1+(g_{m2}+g_{mb2})r_{\alpha 3}]r_{\alpha 2}+r_{\alpha 3}, \tag{3}\]  
where R\({}_{\rm D}\) represents the output impedance of the cascode NM\({}_{2}\) and NM\({}_{3}\), R\({}_{\rm I}\) represents the shunt resistance of the inductor, C\({}_{\rm cr}\) represents the sum of various parasitic capacitances seen from the output. The value of L should be large to increase output power and make ZTX in inductive region in Smith chart, as shown in Figure 4a. Therefore, ZTX can be simplified as a resistor R\({}_{\rm t}\) shunted with an inductor L\({}_{\rm t}\), and the admittance YTX can be written as:  
\[Y_{TX}=\frac{1}{R_{t}}-j\frac{1}{\omega L_{t}}=(\frac{1}{R_{D}}+\frac{1}{R_{I }}+\frac{1}{R_{RL}})-j\bigg{[}\frac{1}{\omega L_{1}}-\omega C_{cr}-\omega C_{ RL}\bigg{]}, \tag{4}\]  
Two additional matching components help to match ZTX to 50 \(\Omega\). Taking the compatibility with the RX matching network (mentioned below) into account, the matching network of a series capacitor C\({}_{1}\) and a shunt capacitor C\({}_{2}\) is selected. ZTX1 is the series impedance of ZTX and C\({}_{1}\), and YTX2 is the shunt admittance of ZTX1 and C\({}_{2}\), which are written as:  
\[Z_{TX1}=\frac{jR_{1}\omega L_{t}}{R_{t}+j\omega L_{t}}+\frac{1}{j\omega C_{1}}, \tag{5}\]\[Y_{TX2}=\frac{1}{Z_{TX1}}+j\omega C_{2}+j\omega C_{dio}, \tag{6}\]  
where \(C_{dio}\) represents the capacitance introduced by ESD diode. From (5) and (6), the value of \(C_{1}\) and \(C_{2}\) can be obtained if the output impedance is matched to 50 \(\Omega\), and Figure 4a shows the trajectory of the \(Z_{TX}\) when applying \(C_{1}\) and \(C_{2}\). Another factor needs to be considered is bonding wire which can be simply modeled as two capacitors shunted with an inductor. The inductance of the bonding wire can be cancelled by its resonating with the output decoupling cap \(C_{4}\) at 2.45 GHz. As shown in Figure 4b, the overall simulated TX impedance \(S_{11}\) is smaller than \(-18\) dB within in ISM band.