A basic light exercise is the back lift. If you are doing spinal flexion exercises for your abs (e.g. crunches), then it's good to balance these with some spinal extension using a back lift.
For serious back strength, I doubt there's a better exercise than the deadlift. This eventually involves very heavy weights, and therefore demands proper instruction in person. Done well this could develop a very strong and safe back; done badly it could cripple you.
In terms of general strength training as mentioned Deadlifts are the best. You do not have to use very heavy weights. Even as your back strength increases you can simply use the same weights as conditioning training. Deadlifts also strengthen your legs, shoulders, arms and grip strength. Like squats it is a fantastic body workout aswell as targeting a particular muscle group.
Be sure to either do your research on correct deadlift "form" or even better speak to a gym trainer who can show you exactly what to do. lifting weights incorrectly is a sure way for injury or incorrect muscle development.
Not sure if you've ever considered weight training, but there are exercises I've done that have made my back strong. If you'd like, try deadlifts, squats, and pullups. (Squats are not only good for your legs, but they do help out your lower back.) Any google search for these weight exercises will help, just make sure you perfect your form first. It may take awhile, but it does help when playing badminton.
If you'd like a more natural method of training your back, then my suggestion would be to practice your over-the-head forehead smashes. This helps out the lattes on your back and you may feel stronger with each session. Side to side pushups are also a good exercise.
Talk to your gym teacher, speak to your family doctor, call Tiger Wood's trainer, ask Michael Phelps coach or visit your local hospital.
I personally do plank exercises - it's been very effective for me, it strengthens the abs and the lower back. I also maintain an upright sitting posture while working. Add that to your cardio exercises like badminton, and you'll have a strong back (and 6 packs) in no time =)