# Appendix b - estimating r, For some typical gate-drive circuits – Fairchild SEMICONDUCTOR AN-7502 User Manual

## Page 7 Application Note 7502 Rev. A1

Turn-On

State 1: MOS Off, JFET Off

I

PK1

= V

G

/R

O

State 2: MOS Active, JFET Active

I

PK2

= (V

G

- V

GS(TH)

)/R

O

State 3: MOS Active, JFET Saturated

I

PK3

= (V

G

- V

G(SAT)

)/R

O

Turn-Off

State 4: MOS Saturated, JFET Saturated

I

PK4

= V

G

/R

O

State 5: MOS Active, JFET Saturated

I

PK5

= V

G(SAT)

/R

O

State 6: MOS Active, JFET Active

I

PK6

= V

G(SAT)

/R

O

The equivalent circuit of Figure A-1 predicts that:

dV

D

/dt = (-g

M

R

L

(V

G

- V

GS(TH)

)e

-t/T1

) /T1

where T1 = R

O

C

GS

+ (1 + g

M

/g

MJ

)R

O

C

X

Note that g

M

R

L

(V

G

- V

GS(TH)

) is usually an order of magnitude

greater than V

DD

, indicating that the drain voltage is discharg-

ing toward a very large negative value. The device operation,
then, is on the early, almost linear, portion of the exponential,
where e

-t/T1

approximates unity. The drain current of Figure A-

2, and hence the drain voltage, does indeed exhibit a linear
decrease with time.

Thus, for state 2:

where I

PK2

= (V

G

- V

GS(TH)

)/R

O

State 3: Mos Active, JFET Saturated

Because of the Miller effect, the gate voltage and, hence, the
gate current, is almost constant during the tail time. The
equivalent circuit then predicts:

State 4: Mos Saturated, JFET Saturated (Turn-off)

Both equivalent-circuit generators are short circuits, and the
gate drive is discharging C

X

in parallel with C

GS

through R

O

.

t = R

O

(C

GS

+ C

X

) ln[V

G

/V

G(SAT)

]

I

PK4

= V

G

/R

O

State 5: Mos Active, JFET Saturated

The JFET current generator V

x

g

mJ

, is operative.

I

PK5

= V

G(SAT)

/R

O

State 6: Mos Active, JFET Active

The Miller effect is now reduced by the activation of V

G

g

MJ

,

and the equivalent circuit predicts:

I

PAK6

= V

G(SAT)

/R

O

Appendix B - Estimating R

O

for Some

Typical Gate-Drive Circuits

Case 1: Typical Pulse-Generator Drive, Figure B-1

FIGURE B-1.

TYPICAL PULSE-GENERATOR DRIVE CIRCUIT

Turn-On and Turn-Off

R

O

= R

GEN

R

GS

/(R

GEN

+ R

GS

)

For the typical case where R

GEN

= 50

, and a coaxial-cable

termination of 50 ohms, R

O

= 25

and V

G

= V

GEN

/2.

Case 2: Voltage-Follower Gate Drive, Figure B-2

FIGURE B-2. VOLTAGE-FOLLOWER GATE-DRIVE CIRCUIT

Turn-On

R

O

is approximately equal to 1/g

M

for R

S

very much

greater than 1/g

M

.

gm = transconductance of driving MOSFET transistor.

Turn Off

R

O

= R

S

t =

[V

DD

- V

DK

][C

GS

+ C

X

(1 + g

M

/g

MJ

)]

g

M

R

L

I

PK2

dV

D

=

g

M

R

L

l

G

=

l

G

dt

C

GS

+ (1 + g

M

R

L

)C

X

C

X

l

G

= I

PK3

= (V

G

- V

G(SAT)

)/R

O

and

t =

(V

DK

- V

D[SAT]

)C

x

I

PK3

t =

[V

DK

- V

D[SAT]

)C

X

I

PK5

t =

[V

DD

- V

DK

][C

GS

+ C

X

(1 + g

M

/g

MJ

)]

g

M

R

L

I

PAK6

V

GEN

R

GEN

V

G

V

DD

R

L

R

GS

+

R

S

V

DD

R

L

Application Note 7502