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partity-time_symmetric_wpt [2025/07/07 14:11] – [Current and voltage ratio] klpartity-time_symmetric_wpt [2025/07/07 14:27] (current) – [Efficiency] kl
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 For $k<k_c$, the self resonant frequency, $\omega_{o3}=\omega_0$, remains the only resonance frequency in the system. From equation (4), it can be seen that the negative resistor is dependent on the coupling factor $k$ and does not automatically compensates the resistances in the network. For $k<k_c$, the self resonant frequency, $\omega_{o3}=\omega_0$, remains the only resonance frequency in the system. From equation (4), it can be seen that the negative resistor is dependent on the coupling factor $k$ and does not automatically compensates the resistances in the network.
  
-FIGURE k vs frequency (e..g, FIG 3.5) HERE?+{{ :0:pt-symmetric_frequency.png?600 |}} 
 + 
  
 The same conclusions can be drawn for the PP compensated circuit. The same conclusions can be drawn for the PP compensated circuit.
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 Analogously, we get for the power transfer efficiency $\eta$: Analogously, we get for the power transfer efficiency $\eta$:
  
-$$ \eta=\frac{L_1R_L}{L_2R_1+L_1(R_2+R_L} $$+$$ \eta=\frac{L_1R_L}{L_2R_1+L_1(R_2+R_L)} $$
  
 These two equations indicitate the important aspect of parity-time symmetric WPT: both the output power and efficiency are constant, i.e., independent on the coupling factor $k$, in the exact symmetric PT-region ($k \geq k_c$). These two equations indicitate the important aspect of parity-time symmetric WPT: both the output power and efficiency are constant, i.e., independent on the coupling factor $k$, in the exact symmetric PT-region ($k \geq k_c$).
 +
 +The underlying explanation is that in a PT-symmetric region, the eigenvalues of the system are pure imaginary. As a result, even when losses are present, there is no change in the eigenstates of the system. 
  
 ===Broken PT-symmetric state=== ===Broken PT-symmetric state===
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 This is not the case in the broken PT-symmetric region, when $k<k_c$. Taken into account the value for the negative resistor in the broken PT-symmetric region, equation (4), and the self-resonance frequency $\omega_{o3}=\omega_0$, it can be calculated that This is not the case in the broken PT-symmetric region, when $k<k_c$. Taken into account the value for the negative resistor in the broken PT-symmetric region, equation (4), and the self-resonance frequency $\omega_{o3}=\omega_0$, it can be calculated that
  
-$$ P_L=\frac{\omega_0^2k^2L_1L_2R_LU_{in}^2}{[\omega_0^2k^2L_1L_2+R_1(R_2+R_L)]^2}$$+$$ P_L=\frac{\omega_0^2k^2L_1L_2R_LV_{1}^2}{[\omega_0^2k^2L_1L_2+R_1(R_2+R_L)]^2}$$
  
 $$ \eta=\frac{\omega_0^2k^2L_1L_2R_L}{R_1(R_2+R_L)^2+\omega_0^2k^2L_1L_2(R_2+R_L)}$$ $$ \eta=\frac{\omega_0^2k^2L_1L_2R_L}{R_1(R_2+R_L)^2+\omega_0^2k^2L_1L_2(R_2+R_L)}$$
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 We can see that now both the output power and efficiency are NOT constant; they change with varying coupling factor $k$. We can see that now both the output power and efficiency are NOT constant; they change with varying coupling factor $k$.
  
-FIGUUR 3.6 HIER? +In the broken PT-symmetric region, the eigenstate amplitude increases or decays exponentially, i.e., no stable region is obtained.
- +
-PT-symmetric: eigenvalues are pure imaginary => even when there are losses present, no change in the eigenstates in time + energy distribution of the mode on both transmitting and receiving sides is mirror-symmetrical. +
- +
-Broken PT-symmetric: eigenstate amplitude increases or decays exponentially+
  
 +{{ :0:pt-symmetric_power_and_efficiency.png?600 |}}
  
-====Efficiency==== 
  
  
partity-time_symmetric_wpt.1751897492.txt.gz · Last modified: by kl