# How to determine the -3dB frequency of a system
**URL:** https://discourse.julialang.org/t/how-to-determine-the-3db-frequency-of-a-system/99755
**Category:** Modelling & Simulations
**Tags:** control, controlsystems
**Created:** [June 2, 2023, 8:39am UTC](https://discourse.julialang.org/t/how-to-determine-the-3db-frequency-of-a-system/99755 "2023-06-02T08:39:46Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [June 2, 2023, 8:39am UTC](https://discourse.julialang.org/t/how-to-determine-the-3db-frequency-of-a-system/99755/1 "2023-06-02T08:39:46Z")
I have the following system, controlled with a PI controller:
```julia
using ControlSystemsBase, Plots
P_sc = 4.42616018443722e6
I_sc = 11838.3957271545*4
P = tf(-1.898e-8, [1, 0.01934])
C = -pid(P_sc, I_sc)
PC = feedback(P*C)
```
I can create a bodeplot of the plant or the feedback system, but how can I get the -3db frequency as a number?
---
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [June 2, 2023, 10:11am UTC](https://discourse.julialang.org/t/how-to-determine-the-3db-frequency-of-a-system/99755/2 "2023-06-02T10:11:45Z")
OK, first I need the DC gain. I use this function to determine it:
```julia
function dc_gain(sys)
sys.matrix[1].num[0] / sys.matrix[1].den[0]
end
```
I guess this will not work for all types of systems, not sure for which it works and for which not…
---
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [June 2, 2023, 10:35am UTC](https://discourse.julialang.org/t/how-to-determine-the-3db-frequency-of-a-system/99755/3 "2023-06-02T10:35:04Z")
OK, this code does what I want, but I would be pleased for any comments how to improve it:
```julia
using ControlSystemsBase, Roots
P = tf(-1.898e-8, [1, 0.01934])
function dc_gain(sys)
sys.matrix[1].num[0] / sys.matrix[1].den[0]
end
# calculate the 3db bandwidth of a low-pass like system
function w_3db(sys)
gain_3db = abs(dc_gain(sys)) * exp10(-3/20)
function res(w)
mag = bode(sys, [w])[1][1]
mag - gain_3db
end
res = find_zero(res, (exp10(-4), exp10(1)))
return res
end
println(w_3db(P))
```
---
### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [June 2, 2023, 1:24pm UTC](https://discourse.julialang.org/t/how-to-determine-the-3db-frequency-of-a-system/99755/4 "2023-06-02T13:24:13Z")
Is there anything wrong with the built-in `dcgain`?
---
### Author:  [@ufechner7](https://discourse.julialang.org/u/ufechner7)
#### Post date: [June 2, 2023, 4:06pm UTC](https://discourse.julialang.org/t/how-to-determine-the-3db-frequency-of-a-system/99755/5 "2023-06-02T16:06:44Z")
Nothing wrong with it, just that I did not know that it exists…
```julia
dcgain(sys)[1]
```
works also fine…