# Cascade multiple Full-bridge Rectifiers Connected to Multiple AC Sources

I want to rectify multiple isolated AC signals (Generated from multiple wireless power receiving coils) to a single DC load. For example, consider the following the schematic with two voltage sources $$\V_1\$$ and $$\V_2\$$ representing two wireless power receiving coils. $$\V_1\$$ and $$\V_2\$$ are at the same frequency (say around $$\500~\rm{kHz}\$$) and same phase.

simulate this circuit – Schematic created using CircuitLab

Question One:(solved more or less from the answer by @AndyAka and the other comments)

1. Will this circuit works even if the magnitudes of $$\V_1\$$ and $$\V_2\$$ vary significantly? For instance, the magnitude of both sources can vary between $$\5\$$ V to $$\20\$$V independently. Is there any better topology?

Question Two

2. How do we calculate effective AC load impedances seen by two sources (i.e. $$\R_{L1}\$$ and $$\R_{L2}\$$)?

For example, if we have a single rectifier, we know its equivalent ac-side impedance is $$\\frac{\pi^2 R_L}{8}\$$[reference]. Now the question is, how can we calculate the equivalent impedance seen by two AC sides (see schematic $$\R_{L1}\$$ and $$\R_{L2}\$$)?

Here is my approach so far: Both ac links will have the same current. Therefore, equivalent load impedances should be proportional to the voltages, i.e. $$\\frac{R_{L1}}{R_{L2}}=\frac{V_1}{V_2}\$$. But what will be their values? is $$\R_{L1}+R_{L2}=\dfrac{\pi^2 R_L}{8}\$$? If this way of calculation is correct, I have another problem because of my $$\V_1\$$ and $$\V_2\$$ also dependent on the equivalent load impedances $$\R_{L1}\$$ and $$\R_{L2}\$$. In this case, do I have to use an iterative method to solve this problem?

• Since V1 and V2 are in-phase, why not simply connect them in series and use one bridge rectifier? – Bimpelrekkie Nov 4 '19 at 8:07
• @Bimpelrekkie, Thanks, two reasons: First, as two sources represent WPT coils, there may be reverse power flow (one coil to another) when they are connected in the AC side. Second, they may not be exactly in-phase - there may be a slight phase difference in real implementation. Will give it a try though. – Pojj Nov 4 '19 at 8:20

Observations:

• With the bridge rectifiers in series, if (say) V2 was quite active and (say) V1 was close to zero volts, the DC output would be 4 diode drops down on the AC voltage and this is worse than just collecting energy from V2 and its bridge rectifier.
• Having the bridge outputs in parallel means you always collect "decent" energy even if only 1 source is active but, the down side is that you only collect energy from 1 source (that source being the one with the largest amplitude).
• If the receive coils are individually resonant tuned (using parallel capacitors) then you might consider having all receive windings in series and one parallel tuning capacitor.

I would urge you to do simulations as this will tell you a lot and, the number of scenarios that can be tested will prove to be a better source of what you need to know than my limited set of observations. If this was my project, I'd be simulating it to death because IT WILL provide decent and real-world repeatable results.

• Thanks for the points. This replies to my question one. Indeed, I did simulations for both series and parallel combinations and found that series one is better with practical settings. How about Question 2? – Pojj Nov 4 '19 at 9:09
• I only see RL - no sight of RL1 and RL2. – Andy aka Nov 4 '19 at 9:17
• Do you mean equivalent AC load seen by both sources is same i.e. $R_{L-ac} = \pi^2 R_L/8$? But when two voltages are different, should it should be $R_{L-ac} \frac{V_{1,2}}{V_1+V_2}$? Then the question is, will R_{L-ac} same as single rectifier case? (I will edit the question to add these details) – Pojj Nov 4 '19 at 9:46
• Go the easy route and use a simulator is my strong advice. – Andy aka Nov 4 '19 at 13:04
• The diode drop issue can be addressed by using virtual diodes. They're getting popular for applications like this. – MadHatter Nov 4 '19 at 13:17