Simple RC–CR Network | IQ Signal Basics

 I came across old post about phase shifting circuit. It immediately brought back to my engineering study in communication system. In the book there I/Q modulators were shown as a simple box, I mean no circuit schematic and how to built those modulators. In one of them I saw the Hilbert Transform block and I just didn't know how to make a physical circuit of Hilbert Transform. So after many years, I am still trying to figure out many electronics circuits. When I wrote about op-amp based phase shifting circuit, I thought knowing this is enough. I looked for alternative circuit and come across the RC–CR Network. Here, I want to write down note on this.

RC CR Network Circuit Diagram

For resistors and capacitors R1=R2=R  and C1=C2=C.

How to find this resistors and capacitors value.

Exact 90° phase difference occurs at:

$$RC=\frac{1}{2\pi \mathrm{f}}$$

For:

$$f = 1\,kHz$$
$$RC=\frac{1}{2\pi (1000)}\approx 159\mu s$$

Let’s choose practical values:

$$C=0.1\mu F$$

Then:

$$R = \frac{159\mu s}{0.01\mu F}$$ $$R\approx 1.9k\mathrm{\Omega }$$

Use standard value:

✅ R = 1.6 kΩ
✅ C = 10 microF