SME
Electronics · Problem type
Schmitt-trigger thresholds
Use this for “An inverting Schmitt trigger has ±12 V rails, R₁ = 10 kΩ and R₂ = 50 kΩ. Find its thresholds.”
Diagram
VTH
=
VₛₐₜR₁
R₁ + R₂
VTH
=
12
V
×
10
kΩ
10 kΩ + 50 kΩ
=
2
V
VH = 2·VTH = 4 V
Positive feedback: the output sits at a rail.
Rising past +VTH it drops to −Vₛₐₜ; falling past −VTH it jumps back.
Between them it remembers.
This is an example. Type your own values to start a new problem.
VTH (V)
=
Vₛₐₜ (V)
×
R₁ (kΩ)
R₁ (kΩ)
+
R₂ (kΩ)
VH (V)
=
2
×
VTH (V)
Formulas
VTH
=
Vₛₐₜ
×
R₁
R₁
+
R₂
2
=
12
×
10
10 + 50
VH = 2 × VTH
4 = 2 × 2
Assumptions
•
Positive feedback holds the output at +Vₛₐₜ or −Vₛₐₜ, with no linear range between.
•
R₁ (to ground) and R₂ (from the output) divide the output down to the + input: that is the threshold.
•
The input drives the − input, so rising past +VTH sends the output low and falling past −VTH sends it high.
Step-by-step
WE KNOW
Vₛₐₜ = 12 V, R₁ = 10 kΩ, R₂ = 50 kΩ
FIND
threshold (VTH), hysteresis width (VH)
Step 1 · Find threshold (VTH)
Use VTH = Vₛₐₜ × R₁ ÷ (R₁ + R₂)
The divider’s share of the rail reaches the + input.
VTH
=
12
×
10
10 + 50
VTH
=
12
×
10
60
VTH
=
120
60
VTH = 2 V
Step 2 · Find hysteresis width (VH)
Use VH = 2 × VTH
The loop runs from −VTH to +VTH.
VH = 2 × 2
VH = 4 V
Check
Put the numbers back in. Both sides should match.
2
=
12
×
10
10 + 50
✓
4 = 2 × 2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.