I am new to PCB design. My circuit contain a voltage of 3.3V, maximum signal frequency of 400 kHz and less than 10 components connected to ground. Do I really need a ground plane in my PCB? Or to be precise: When should I use a ground plane?
A lot depends on whether you are doing a commercial PCB to be manufactured and sold, or a few one-off boards for your own use. If the former, then a ground plan is more important to keep radiated emissions down to meet FCC (Part 15, unintentional radiators), CE and other regulations, although I've seen plenty of commercial products with one or two-sided boards and no-ground planes. (On the other hand, one of my clients just made a six-layer board with three signal layers, a Vcc layer, and two ground planes in a sandwich configuration.)
If you only have signals up to 400 kHz, then it sounds like you aren't using a microcontroller (or if you are, you are using an internal oscillator so there is no crystal). If you have prototyped your circuit on a wireless breadboard or the like, and it works okay, then it should work fine without a ground plane.
Even if you are doing a commercial product, if your device is battery powered, and it has no signals above 1.705 MHz (which is true in your case), then it is exempt from FCC rules.
First, you need to make sure that your assumptions are valid. For example, if your circuit is connected to two pieces of equipment powered by switch mode supplies, there will be a common-mode high frequency current flowing between those units. The current will flow through your device, generating "noise" voltages on the impedances of the traces in your circuit.
Secondly: whether it's a problem or not depends solely on what the circuit is doing. You need to estimate the impedances of the traces between various nodes in the circuit, and model their effect on the circuit. If you're using a circuit modeling tool such as spice, you should replace your "solid" connections with circuits equivalent to trace impedances. You can then determine if the voltages dropped across those impedances are an issue or not.
Idealy you should always use a ground plane. But for different kind of reason it is not always possible or suitable:
- 1 and 2 layer(s) PCB:
For 1 layer, I think the reason is quite obvious. You can fill the unrouted PCB with copper to GND but that's not a real ground plane.
For two layers, you don't always have enough space for routing on one layer and a ground plane on the other, but if you can, do it, even if you have some small traces on the ground plane layer.
- Analog design:
Some analog design should not be referenced to a ground plane or should have a star connection for GND.
For instance, if you're doing an acquisition circuit, you should worry about the different reference planes. Same for isolated power supplies.
Also it depends of your design, if you're doing a 5V CMOS level design, disturbances like 1V spikes may not affect your circuit's behavior, while with a 1.8V, it become quite harmful for the behavior.
Same for frequency and rise time: a low-speed circuit won't spread too much EMC comparing to high-speed circuits (I'm not talking about the signal frequency, but about the rise time equivalent frequency).