All transistors in the above circuit have the same size. Which option below shows the correct relationship between the currents Iref and Io.[Fill in the blank]单项选择题
A
a. Iref = I2 +I0
B
b. I0 = Iref +I2
C
c. I0 = BetaxIref
D
d. Iref = I2 =I0

Question

All transistors in the above circuit have the same size. Which option below shows the correct relationship between the currents Iref and Io.[Fill in the blank]

BlackTom AI · Accepted Answer

Kirchhoff’s current law at the branching node gives the central relationship: the input reference current must equal the sum of the currents leaving that node. The relevant knowledge points are: (1) KCL (sum of currents into a node = sum out); (2) a current mirror sets transistor VGS but actual branch currents obey node current balance; (3) identical transistor sizes only make mirrored branches behave similarly, they do not change KCL.

Step-by-step reasoning:
1. Identify the node where Iref arrives and then divides into two branches carrying I2 and Io. All transistor drains/sources tied at that node mean currents entering and leaving that node must balance.
2. Apply KCL algebraically: current into node (Iref) minus currents leaving the node (I2 and Io) equals zero. So Iref − I2 − Io = 0.
3. Rearranging yields Iref = I2 + Io. This is the exact algebraic expression from KCL and requires no additional device parameters.

Intermediate step shown:
Iref − I2 − Io = 0
=> Iref = I2 + Io

Why this is correct: regardless of transistor matching, currents at a node must sum to zero; identical device sizes only affect how I2 and Io compare to each other or to a mirror reference but do not alter the node-current balance. If the mirror bias supplies a single current that then splits among two output transistors, the sum of those outputs must equal the bias.

Why the other choices are incorrect:
- b (Io = Iref + I2) violates KCL sign/direction (it would imply currents are generated rather than split).
- c (Io = Beta × Iref) incorrectly applies a bipolar current gain concept (β) not given and not applicable to MOS current mirror sizing as stated.
- d (Iref = I2 = Io) would only hold if separate identical currents were each provided by independent identical sources; with a single reference feeding two branches that share the node, the reference is the sum, not equal to each individually.

Conclusion: The correct relationship is Iref = I2 + Io, confirming answer (a).

All transistors in the above circuit have the same size. Which option below shows the correct relationship between the currents Iref and Io.[Fill in the blank]单项选择题

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