Learn Analog Circuits with Zundamon

Episode 4

Current Mirrors and Active Loads

Increasing the load resistor stopped the amplifier from working. Learn how current mirrors and active loads provide high gain while preserving the bias current.

Watch on YouTube (6:46)
  • Shikoku Metan (explains)
  • Zundamon (asks)

1Intro: why did a larger RD stop amplification?

Zundamon

My design is in trouble! I increased RD for more gain, and it stopped amplifying!

Illustration: My design is in trouble! I increased RD for more gain, and it stopped amplifying!
Figure 1

Shikoku Metan

Use a transistor load instead of a resistor. We'll use current mirrors and PMOS.

Illustration: Use a transistor load instead of a resistor. We'll use current mirrors and PMOS.
Figure 2

Zundamon

Please! I need to fix it before the deadline, nanoda!

Illustration: Please! I need to fix it before the deadline, nanoda!
Figure 3

2Review: increasing RD

Shikoku Metan

Recall common-source gain: Av = −gm(RD∥ro).

Illustration: Recall common-source gain: Av = −gm(RD∥ro).
Figure 4

Zundamon

I thought a larger RD would give more gain.

Shikoku Metan

Make RD ten times larger: 50 kΩ. At episode three's current of about 0.18 mA, the drop would be about 9 V.

Illustration: Make RD ten times larger: 50 kΩ. At episode three's current of about 0.18 mA, the drop would be about 9 V.
Figure 5

Zundamon

But the supply is only 1.8 V! That's nowhere near enough!

Illustration: But the supply is only 1.8 V! That's nowhere near enough!
Figure 6

Shikoku Metan

With a resistor, raising the small-signal resistance also raises the DC voltage drop. The two can't be separated.

Illustration: With a resistor, raising the small-signal resistance also raises the DC voltage drop. The two can't be separated.
Figure 7

3Using a current source as the load

Shikoku Metan

We want fixed DC current with a high small-signal resistance.

Illustration: We want fixed DC current with a high small-signal resistance.
Figure 8

ZundamonQuestion

You mean a current source?

Shikoku Metan

Right. In episode three, a DC current source became a small-signal open circuit.

Shikoku Metan: Replace RD with an ideal current source. For small signals it's open, so RD∥ro becomes just ro, and Av = −gm·ro, the intrinsic gain itself.

Illustration: Replace RD with an ideal current source. For small signals it's open, so RD∥ro becomes just ro, and Av = −gm·ro, the intrinsic gain itself.
Figure 9

ZundamonQuestion

How do we build such a current source?

4Creating a current source with a diode connection

Shikoku Metan

A saturated MOSFET is a current source controlled by VGS.

Illustration: A saturated MOSFET is a current source controlled by VGS.
Figure 10

ZundamonQuestion

How do we find the VGS that gives the current we want?

Shikoku Metan

Connect the gate to the drain. This is called a diode connection.

Shikoku Metan: Feed in a reference current, Iref, from outside.

Illustration: Feed in a reference current, Iref, from outside.
Figure 11

Shikoku Metan

The MOSFET then establishes the VGS that carries exactly Iref.

ZundamonQuestion

Is it still in saturation with gate and drain connected?

Illustration: Is it still in saturation with gate and drain connected?
Figure 12

Shikoku Metan

Yes. Saturation needs VDS ≥ VGS−Vth. With VDS=VGS, that holds whenever VGS exceeds Vth.

Shikoku Metan: For Iref=0.1 mA, VGS is about 0.70 V.

5The current mirror

Shikoku Metan

Add a second MOSFET and connect their gates together.

Illustration: Add a second MOSFET and connect their gates together.
Figure 13

Shikoku Metan

Same size, meaning the same W/L, and the same VGS, so the right-hand device carries the same current.

Shikoku Metan: It copies like a mirror, so it's a current mirror. Call the output current Iout.

Shikoku Metan: Double the right-hand W/L and Iout doubles to 0.2 mA.

Illustration: Double the right-hand W/L and Iout doubles to 0.2 mA.
Figure 14

Shikoku Metan

Because ID is proportional to W/L. That assumes Vth and the other parameters match, and that both VDS are equal.

6Mirror error from ro and the saturation condition

ZundamonQuestion

So it's exactly the same current whatever circuit we connect on the right?

Illustration: So it's exactly the same current whatever circuit we connect on the right?
Figure 15

Shikoku Metan

Not necessarily. First, return both devices to the same W/L.

Illustration: Not necessarily. First, return both devices to the same W/L.
Figure 16

Shikoku Metan

The left device's VDS is about 0.70 V, since VDS=VGS. The right one's VDS depends on whatever circuit it drives.

Shikoku Metan: At right VDS=1.5 V, Iout≈0.107 mA, about seven percent higher.

Illustration: At right VDS = 1.5 V, Iout ≈ 0.107 mA, about seven percent higher.
Figure 17

Shikoku Metan

The slope of this graph is the 1/ro from episode two. Iout equals Iref only when both devices have the same VDS.

Illustration: The slope of this graph is the 1/ro from episode two. Iout equals Iref only when both devices have the same VDS.
Figure 18

Shikoku Metan

Too little VDS is also a problem: at 0.2 V, Iout≈0.080 mA, outside saturation.

Shikoku Metan: So keep the output device saturated too. Here Vov=0.70−0.4=0.3 V, so VDS must be about 0.3 V or more.

7A closer look at PMOS

ZundamonQuestion

Can we just put that mirror in place of RD?

Illustration: Can we just put that mirror in place of RD?
Figure 19

Shikoku Metan

The load sits between VDD and the output. With an NMOS there, its source would be the output node, so VGS would move with the output and the current wouldn't stay constant.

Illustration: The load sits between VDD and the output. With an NMOS there, its source would be the output node, so VGS would move with the output and the current wouldn't stay constant.
Figure 20

Shikoku Metan

Use the PMOS from episode one. Its source can connect to VDD.

Illustration: Use the PMOS from episode one. Its source can connect to VDD.
Figure 21

Shikoku Metan

Its source arrow points inward, with a circle at the gate and source on top.

Shikoku Metan: It turns on with the gate below the source, so use VSG.

Illustration: It turns on with the gate below the source, so use VSG.
Figure 22

Shikoku Metan

When VSG exceeds |Vth|, current flows from source to drain, top to bottom.

Shikoku Metan: Use the NMOS equations with VSG, VSD, and |Vth|; positive current runs S to D.

Illustration: Use the NMOS equations with VSG, VSD, and |Vth|; positive current runs S to D.
Figure 23

ZundamonQuestion

Is the current magnitude the same as NMOS too?

Shikoku Metan

Holes move less easily than electrons. In this model, for the same W/L, K is halved to 1 mA/V².

Illustration: Holes move less easily than electrons. In this model, for the same W/L, K is halved to 1 mA/V².
Figure 24

Shikoku Metan

A PMOS mirror works too, like the NMOS mirror flipped upside down.

Illustration: A PMOS mirror works too, like the NMOS mirror flipped upside down.
Figure 25

8The common-source amplifier with an active load

Shikoku Metan

Use that PMOS mirror as the load. A transistor load is called an active load.

Illustration: Use that PMOS mirror as the load. A transistor load is called an active load.
Figure 26

Shikoku Metan

M1 amplifies, M2 is the load, and diode-connected M3 receives Iref.

Shikoku Metan: VDD=1.8 V, Iref=0.1 mA. M2 and M3 match; each body is tied to its source.

Illustration: VDD = 1.8 V, Iref = 0.1 mA. M2 and M3 match; each body is tied to its source.
Figure 27

Shikoku Metan

VOUT is where M1 and M2 carry equal current. Overlay their curves.

Illustration: VOUT is where M1 and M2 carry equal current. Overlay their curves.
Figure 28

Zundamon

The intersection is the operating point!

Shikoku Metan

For VOUT=0.9 V, VIN is about 0.70 V and current about 0.1 mA.

Shikoku Metan: Sweeping VIN gives this transfer curve. Much steeper than episode three's resistor load, the dotted line.

Illustration: Sweeping VIN gives this transfer curve. Much steeper than episode three's resistor load, the dotted line.
Figure 29

9Small-signal equivalent circuit and Av

Shikoku Metan

Let's derive the gain by transforming the small-signal circuit.

Shikoku Metan: We assume both M1 and M2 are saturated. That holds while the output stays between about 0.3 V, M1's Vov, and about 1.4 V, which is VDD minus M2's Vov.

Illustration: We assume both M1 and M2 are saturated. That holds while the output stays between about 0.3 V, M1's Vov, and about 1.4 V, which is VDD minus M2's Vov.
Figure 30

Shikoku Metan

Step one: short the DC voltages and open the reference current source.

Illustration: Step one: short the DC voltages and open the reference current source.
Figure 31

ZundamonQuestion

Doesn't opening Iref leave M2's gate floating?

Shikoku Metan

No. M3 is the diode connection from episode three: for small signals it's a resistance of about 1/gm3, tying M2's gate to ground.

Illustration: No. M3 is the diode connection from episode three: for small signals it's a resistance of about 1/gm3, tying M2's gate to ground.
Figure 32

Shikoku Metan

No signal reaches that node, so M2's gate signal is zero. Its source sits at VDD, also signal ground, so vsg2=0.

Shikoku Metan: Step two: gm2·vsg2=0, leaving only ro2 in M2's model.

Zundamon

So the current-source load looks like resistance ro2 for small signals!

Illustration: So the current-source load looks like resistance ro2 for small signals!
Figure 33

Shikoku Metan

M1 is the same as before: a gm1·vin source in parallel with ro1.

Illustration: M1 is the same as before: a gm1·vin source in parallel with ro1.
Figure 34

Shikoku Metan

Step three: ro1 and ro2 both connect output to ground, so they're parallel.

Shikoku Metan: RD has become ro2: Av = −gm1(ro1∥ro2).

Illustration: RD has become ro2: Av = −gm1(ro1∥ro2).
Figure 35

10Intrinsic gain and a numerical example

ZundamonQuestion

How does that compare with gm·ro for an ideal source load?

Shikoku Metan

If ro1=ro2, their parallel resistance halves: Av = −gm·ro/2.

Illustration: If ro1 = ro2, their parallel resistance halves: Av = −gm·ro/2.
Figure 36

Shikoku Metan

The load is a real transistor too. Its finite ro reduces the gain.

Illustration: The load is a real transistor too. Its finite ro reduces the gain.
Figure 37

Shikoku Metan

At the operating point, VIN=0.70 V and VOUT=0.9 V, gm1 is about 0.65 mA/V, and ro1 and ro2 are both about 108 kΩ.

Shikoku Metan: In parallel that's about 54 kΩ, so Av ≈ −35: exactly half of gm1·ro1≈70.

Illustration: In parallel that's about 54 kΩ, so Av ≈ −35: exactly half of gm1·ro1 ≈ 70.
Figure 38

Zundamon

It matches the graph's slope! About nine times episode three's −4!

Illustration: It matches the graph's slope! About nine times episode three's −4!
Figure 39

Shikoku Metan

The bias is different from last time, too. Vov dropped from 0.4 V to about 0.3 V, so the intrinsic gain gm·ro rose from 56 to about 70.

Illustration: The bias is different from last time, too. Vov dropped from 0.4 V to about 0.3 V, so the intrinsic gain gm·ro rose from 56 to about 70.
Figure 40

11Setting the operating point

Shikoku Metan

But beware: a 10 mV VIN change moves VOUT by about 0.35 V.

Illustration: But beware: a 10 mV VIN change moves VOUT by about 0.35 V.
Figure 41

Shikoku Metan

Both current curves are flat, so their intersection moves a long way.

Shikoku Metan: In practice the operating point is set with negative feedback: the output's deviation is fed back to the input to cancel it. More on that in a later episode.

Illustration: In practice the operating point is set with negative feedback: the output's deviation is fed back to the input to cancel it. More on that in a later episode.
Figure 42

12Summary

Shikoku Metan

A current mirror copies current using the VGS set by a diode-connected device.

Shikoku Metan: Reverse the voltage and current conventions, and PMOS uses the same equations.

Illustration: Reverse the voltage and current conventions, and PMOS uses the same equations.
Figure 43

Zundamon

Active-load common-source gain is −gm1(ro1∥ro2), nanoda!

Illustration: Active-load common-source gain is −gm1(ro1∥ro2), nanoda!
Figure 44

Zundamon

More gain with an active load! I'll include the saturation conditions in my report!

Shikoku Metan

Next time: source followers and common-gate stages. Compare all three basics.

Zundamon

Thanks for reading, nanoda!