This article covers some important issues in design of high-frequency electronic circuits and commonly followed practices to mitigate them.
Electronic circuits behave very differently at high frequencies. This is mainly due to a change in the behaviour of passive components (resistors, inductors and capacitors) and parasitic effects on active components, PCB tracks and grounding patterns at high frequencies. The change of behaviour also causes electromagnetic interference (EMI) problems. This article discusses these effects and some commonly followed practices to mitigate them.
Ideal components
Resistor
In time domain, the instantaneous voltage and current for an ideal resistor are related by:
v=iR ——-(1)
where R is the resistance and v the energy lost per unit charge when it flows from positive terminal to negative terminal. The energy lost is converted into heat by the resistor.
In frequency domain, phasors for sinusoidal voltages and currents are related by:
V=IR ———-(2)
Thus the voltage-current relationship is independent of frequency.
Inductor (energy storage element)
In time domain, voltage-current relationship for an ideal inductor is:
v=Ldi/dt ———(3)
where L is the inductance and t the time.
Since v is the energy lost per unit charge, when charge flows from the positive terminal to the negative terminal, this energy is used for increasing current as per the above equation. The magnetic field inside the inductor coil is proportional to the current. Hence the energy is used in building up the magnetic field and stored in the magnetic field.
In frequency domain, phasors for sinusoidal voltages and currents are related by:
V=j(Lω)×I ——–(4)
where L is the inductance in Henry, ω the angular frequency of driving sinusoid voltage source in radians/second and j=√–1
Hence the voltage-current relationship for inductors varies with frequency.
Capacitor (energy storage element)
In time domain, voltage and current for an ideal capacitor are related as:
where q is the charge accumulated on the capacitor at time t, c the capacitance and t the time.
The charge accumulated on the capacitor establishes an electric field between plates of the capacitor and thus the capacitor stores energy in the form of electric field.
In frequency domain, phasors for sinusoidal voltages and currents are related by:
where C is the capacitance in Farad, the angular frequency of driving sinusoid voltage source in radians/second and j=√–1
Hence, the voltage-current relationship for capacitor varies with frequency.
Behaviour of components at high frequencies
Wires
At high frequencies, wires behave as inductors (opposing changes in the current) besides their natural low resistance value.
Resistors
At high frequencies, resistors behave as series inductors (opposing changes in the current) and parallel capacitors (opposing changes in the voltage) besides their natural resistance.
Inductors
At high frequencies, inductors behave as series resistors and parallel capacitors besides their natural inductance.
Capacitors
At high frequencies, capacitors behave as series resistors and series inductors besides their natural capacitance.
Thus, simple voltage/current relationships for ideal components are no longer valid at high frequencies and suitable circuit analysis methods are to be used by replacing them with their high-frequency equivalent circuits.
PCB tracks
PCB tracks behave like wires at low frequencies. This behaviour is no longer sustained at high frequencies. To understand this behaviour, you have to understand how a signal is transmitted from a source to the receiver and transmission line theory. Fig. 8 shows a source/driver delivering signal to a load/receiver through wires (shown by lines).
At low frequencies, connecting wires from the transmitter/source to the receiver/load have very low resistance and act as short-circuit. Voltage from the source is directly applied to the receiver. Any change in voltage at the source is delivered instantaneously at the same time to the receiver. Appropriate current flows from the positive lead of the source through connecting wire and the load and the return wire, to the negative terminal of the source.
The value of current depends on the source voltage and the load.
Normally, source and receivers are components soldered on PCBs and connecting wires are tracks on PCBs. Send and return PCB tracks behave like a transmission line if the signal frequency of the source is sufficiently high.
Lumped transmission line model represents send and return lines to have resistance (R), inductance (L), capacitance (C) and conductance (G) per unit length. Their values depend on spacing between send and return lines, thickness of lines, transmission medium, etc. Since these lines are copper tracks on PCBs, their values are dependent on PCB tracks’ thickness and separation, that is, PCB tracks’ geometry and board material. These parameters cause voltages and currents to travel like waves through transmission lines (PCB tracks).
