## 3 Modified and Simplified T-Type Structure Designed for Low Attenuation Units
### Proposed Structure of the Attenuator with Bypass Compensation Technology  
For phase correction architecture, the two simplest compensation solutions are adding additional series/shunt capacitors at the end of the branches. The modified switched T-type attenuator with a series tail capacitor \(C_{T}\) is shown in Figure 4a. Depending on the equivalent circuit model, the transmission phases in the reference and attenuation modes, respectively, can be calculated as follows:  
\[\theta_{ref,seri}\approx-\tan^{-1}\left(\frac{C_{off}C_{T}\omega Z_{0}}{2 \left(C_{off}+C_{T}\right)}\right) \tag{6}\]  
\[\theta_{att,seri} =-\tan^{-1}\frac{\omega C_{T}\left(1-\omega^{2}C_{T}L_{on}\right) Z_{0}}{\omega^{2}C_{T}^{2}R_{on,all}\left(2R_{on,all}+Z_{0}\right)+2\left(1- \omega^{2}C_{T}L_{on}\right)^{2}} \tag{7}\] \[\approx-\tan^{-1}\frac{K\left(C_{T}\omega\right)}{L\left(\omega C _{T}\right)^{2}+M}\]  
where \(K\), \(L\), and \(M\) are \(\omega\)-independent constants used to simplify the formula, since \(\omega^{2}\)\(C_{T}\)\(L_{on}\) is generally considered to be much less than 1. Based on Equations (6) and (7), it can be concluded that the presence of the tail capacitance significantly affects the transmission phase characteristics of the attenuation mode and changes its polarity. However, the phase effect on the reference mode is relatively insignificant since it has the same power in the numerator and denominator. Therefore, this method can only achieve phase compensation within a relatively narrow percentage bandwidth. Furthermore, using the same analytical approach, another compensation method using a parallel bypass capacitor \(C_{B}\) is shown in Figure 4a, whose transmission phase function can be expressed as  
\[\theta_{ref,paral}\approx-\tan^{-1}\left(\frac{C_{off}\omega\left(C_{B}^{2}R_{ p}^{2}\omega^{2}+1\right)}{2\left(C_{B}^{2}R_{p}^{2}\omega^{2}+2C_{off}C_{B}R_{p}^{2} \omega^{2}+1\right)}\right) \tag{8}\]  
\[\theta_{att,paral}\approx-\tan^{-1}\frac{O\left(C_{B}\omega\right)}{P\left( \omega C_{B}\right)^{2}+Q} \tag{9}\]  
where \(O\), \(P\), and \(Q\) are also constants independent of \(\omega\). The above equations indicate that parallel capacitor \(C_{B}\) can similarly modify the polarity of the attenuation mode and regulate its phase characteristics so as to make it as close as possible to the reference state behavior. Hence, this parallel form performs an improved broadband phase compensation characteristic compared to the tail capacitor, which shows consistency with the results in [32]. In order to demonstrate this difference more intuitively, simulation comparison experiments were performed and the corresponding results are illustrated in Figure 5.  
Here, we take a 0.5 dB unit as an example. The switched transistor was selected as \(1\times 15\) um since smaller sizes have less parasitic inductance and capacitances, which favoring higher bandwidth. From Figure 5b, it can be observed that the broadband compensation effect of \(C_{B}\) is actually superior to that of \(C_{T}\), with the maximum variation decreasing from 0.67\({}^{\circ}\) to 0.09\({}^{\circ}\). Hence, the parallel capacitor structure was finally used for the DSA design.