In order to be able to communicate with the SIM card, you need a device that connects a PC and a SIM card.
The most common, at the same time quite simple and reliable is the "Phoenix".
There are several implementations of it, but they are all basically identical.
The only differences are how complicated the circuit of the hardware itself is.
This affects the stability of the work, but even the simplest assemblies allow you to normally transmit and receive data.
I made my first “Phoenix” a long time ago (several years ago), tried other implementations of it, and settled on one of the schemes that has been working steadily for quite some time.
Data transfer frequency: 3.57 MHz;
Card reset: direct;
Connection: Com Port;
Food: external or Com Port;
Appointment: for communication with SIM cards.
I propose to assemble a scheme that combines the "Phoenix" and "Ludipipo".
The first is already known to you, but the second is a PIC microcontroller programmer.
This combination is successful if only because you do not need two devices for your experiments, you will not need to change the programmer to a reader (or vice versa), depending on the situation.
Despite the fact that the circuit combines two devices, its complexity is not great.
You will need a sheet of foil textolite with a thickness of 1 - 1.5 mm, soldering accessories, iron (III) chloride, and details:
Solder all the details on the board according to the scheme:
You can download all schemes in the form of this archive .