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--- different_power_gains [2024/09/06 20:00] – admin
+++ different_power_gains [2025/03/28 14:06] (current) – 2a02:1812:40f:9800:ddf3:8f43:6dcc:25a9
@@ Line 82: / Line 82: @@
 $$ G_P=\frac{P_{L}}{P_{in}}$$
+Since both $P_L$ and $P_{in}$ are independent on the generator impedance $Z_G$, the operating power gain $G_P$ is also independent on $Z_G$. The generator impedance does not need to be specified: we just need to know how much power got to the network, not how it got there.
+The gain depends on the network $Z$ and on the load value $Z_L$. Obviously, $G_P$ can only be defined if a value for the load $Z_L$ is specified.
+In systems where the goal is to transfer energy from a source to a load, the operating power gain is often called 'the power conversion efficiency', or simply 'the efficiency" of the system.
+===Available gain $G_{A}$===
+The available gain $G_A$ is defined as the ratio of the maximum available load power $P_A$ to the available input power $P_{AG}$:
+$$ G_A=\frac{P_{A}}{P_{AG}}$$
+Since both $P_A$ and $P_{AG}$ are independent on the load impedance $Z_L$, the available gain $G_A$ is also independent on $Z_L$. The gain depends on the network $Z$ and on the generator impedance value $Z_G$.
+Obviously, $G_A$ can only be defined if a value for the generator impedance $Z_G$ is specified.
+===Transducer gain $G_{T}$===
+The transducer gain $G_T$ is defined as the ratio of the power dissipated in the load $Z_L$ to the available input power $P_{AG}$ of the generator:
+$$ G_T=\frac{P_{L}}{P_{AG}}$$
+It is dependent on both the load impedance $Z_L$ and the generator impedance $Z_G$. Both have to be specified in order to be able to define the transducer gain $G_T$.
+===Overview output power within the gains===
+{{:different_power_gains-overview-output-powers.png|}}
+===Overview input power within the gains===
+{{:different_power_gains-overview-input-powers.png|}}
+====Simulation example====
+As example, let us consider a very simple, purely resistive network, consisting of three resistors:
+{{:different_power_gains-example-network.png|}}
+//Figure 6: Simple, purely resistive, example network//
+We simulate the three gains in LT Spice with a DC voltage source of 12 V, as function of the generator resistance and the load resistance.
+{{:different_power_gains-spice-simulation.png|}}
+//Figure 7: Schematics in LT Spice for the three gains, for the example network, with variable load and/or generator resistance {R}.//
+We first simulate the operating power gain $G_P$ as function of the load resistance. This gain is independent on the generator resistance. In the simulation, a generator resistance of 8.02773 ohm was chosen (see further), but this value doesn't matter for the simulation of the operating power gain $G_P$.
+The graph below (green) shows that a maximum of $G_P$ = 10.9% is reached for a load of 14.5 ohm.
+{{:different_power_gains-simulation-graph.png|}}
+//Figure 8: Simulation results of the gains as function of varying generator or load resistance (logarithmic axis) for the given example.//
+Next, the available gain $G_A$ is simulated as function of varying generator resistance (this gains is independent on the value of the load). We find a maximum of 10.9% at a generator resistance of 8.0 ohm.
+Finally, the transducer gain $G_T$ is simulated, first for varying generator resistance, and next for varying load. The generator/load resistance in each non-varying case is chosen to be the optimal value for the other gains. The graphs are identical to the other gains ([[explanation]]). A maximum of 10.9% is found for the optimal generator and load resistance of 8.0 and 14.5 ohm.
+<color #808080>**Some background references**</color>
+  * <color #808080>Egan,W.F. Practical RF System Design; JohnWiley & Sons: Hoboken, NJ, USA, 2003; pp. 313–315. </color>
+  * <color #808080>Mastri, F.; Mongiardo, M.; Monti, G.; Dionigi, M.; Tarricone, L. Gain Expressions for Resonant Inductive Wireless Power Transfer
+Links with One Relay Element. Wireless Power Transfer 2018, 5, 27–41. </color>
+  * <color #808080>Ben Minnaert, Giuseppina Monti, Alessandra Costanzo and Mauro Mongiardo, [[https://www.mdpi.com/2079-9292/10/6/723/pdf|Gain Expressions for Capacitive Wireless Power Transfer with One Electric Field Repeater]]. Electronics 2021, 10, 723.</color>