# How to calculate the impedance of a rectifier?

I am working on RF energy harvesting. Now I am trying to calculate the impedance of the rectifier, in order to do the impedance matching. An antenna (50 ohm) receives RF signal (915 MHz) and finally become DC by the rectifier and stored into the capacitor. simulate this circuit – Schematic created using CircuitLab

In the figure, the value of L1, C1, sensor node needed to be found.

1. How to calculate the impedance of the rectifier?
2. Should I consider the impedance of the wireless sensor node? If needed, how to measure the impedance of the sensor node?
3. Is a DC-DC converter necessary between the C3 and sensor node?
4. As the antenna receive 915MHz rf signal, the frequency of the AC current in the rectifier is also 915MHz?

I had built a rectifier without impedance matching and had done an experiment. I had measured the voltage change of C2,C3 but the result is strange. The voltage of the C3 will remain 2V for about 250ms. However, theoretically, the voltage should be double of the V(c2) which is 100mv.
Another is why the period of the charge time of C2 is 10ms? I thought it should be 1/4 of the period of the AC source (1/915MHz). Or am I misunderstand it? These questions seem to be stupid.. forgive me.. LOL. • You might try a SPICE transient-style simulation (Skyworks gives the diode SPICE model in their data sheet). – glen_geek Apr 1 '19 at 16:28
• Could you please descript more detailed? – penli Apr 2 '19 at 2:06
• The rectifier impedance WILL NOT BE CONSTANT. Assume 1,000 ohms at 0.02milliAmps, 100 ohms at 0.2 milliAmps, 10 ohms at 2 milliAmps. – analogsystemsrf Apr 2 '19 at 3:49
• The diodes I have measured have followed the formula: 45/I'd; ohms/milliamps. I am surprised that microwave diodes could be that much lower and wonder what the difference is. – EinarA Apr 2 '19 at 5:27

## 2 Answers

Is a DC-DC converter necessary between the C3 and sensor node?

These diodes have a reverse breakdown voltage of about one volt, so even if you had a strong RF source, you'll get only about half a volt output for your sensor... diodes have to deal with peak-to-peak RF voltage. If your sensor requires more than half a volt, then a DC-DC converter will be needed.

Should I consider the impedance of the wireless sensor node? If needed, how to measure the impedance of the sensor node?

You show the sensor as an equivalent resistance (this makes sense, because it will absorb power). It is up to you to characterize this resistance, we are told nothing about it. The L1, C1 matching network will need values to deliver maximum power to this resistance.

How to calculate the impedance of the rectifier?

This is rather difficult tp determine, because diodes are non-linear devices. Diodes have a minimum resistance, this one's data sheet says it is 20 ohms. Its "video resistance" is about 5000 ohms, and might represent a maximum. At zero bias, its dynamic resistance is even higher, and depends on temperature. In addition, both diodes do not conduct all the time, which makes their effective resistance higher still.

A SPICE simulation might help choose appropriate L1, C1 values for the matching network. The diode model would look like:

.MODEL Dsms7630 D(IS=5e-6 N=1.05 RS=20 CJO=0.14e-12 TT=1e-11 M=0.4 EG=.69 XTI=2 FC=.5 BV=2 IBV=1e-4 VJ=.34)

• Thanks. For the sensor node, can I measure the U(voltage) and I(current) when it is working. Then using R=U/I to decide it's resistance? I found a paper which describes a model to calculate the impedance of the rectifier without simulation or any equipment. ieeexplore.ieee.org/document/7898468 – penli Apr 2 '19 at 16:00

The first problem to solve is determining the values of C1 and L1. I decided to remove the diodes from the circuit by shorting across them. The 10uF cap is effectively a short at 915MHz, so the remaining circuit has C1 and C2 in parallel. I assume C2 is fixed and I made C1 the same value. I then calculated for L1 for a 50 ohm input impedance which is 8.558nH. I simulated the circuit which verified the 50 ohm impedance. Then I put the diodes back in. At the time I didn't have a model of the diodes so I created one but still found the impedance to be near 50 ohms. I am not saying this is the final answer but it might work as a good first approach.